wave, overtopping, Figure, with, that, waves, run-up, slope, height, water, crest, will, this, Manual, from, vertical, model, EurOtop, flow, which, Wave, berm, structure, used, mean, given, than, slopes, wall, design

Wave Overtopping of Sea Defences

and Related Structures:

Assessment Manual

August 2007

EA Environment Agency, UK

ENW Expertise Netwerk Waterkeren, NL

KFKI Kuratorium für Forschung im Küsteningenieurwesen, DE

www.overtopping-manual.com

EurOtop Manual

i The EurOtop Team

Authors:

T. Pullen (HR Wallingford, UK)

N.W.H. Allsop (HR Wallingford, UK)

T. Bruce (University Edinburgh, UK)

A. Kortenhaus (Leichtweiss Institut, DE)

H. Schüttrumpf (Bundesanstalt für Wasserbau, DE)

J.W. van der Meer (Infram, NL)

Steering group:

C. Mitchel (Environment Agency/DEFRA, UK)

M. Owen (Environment Agency/DEFRA, UK)

D. Thomas (Independent Consultant;Faber Maunsell, UK)

P. van den Berg (Hoogheemraadschap Rijnland, NL – till 2006)

H. van der Sande (Waterschap Zeeuwse Eilanden, NL – from 2006)

M. Klein Breteler (WL | Delft Hydraulics, NL)

D. Schade (Ingenieursbüro Mohn GmbH, DE)

Funding bodies:

This manual was funded in the UK by the Environmental Agency, in Germany

by the German Coastal Engineering Research Council (KFKI), and in the

Netherlands by Rijkswaterstaat, Netherlands Expertise Network on Flood

Protection.

This manual replaces:

EA, 1999. Overtopping of Seawalls. Design and Assessment Manual, HR,

Wallingford Ltd, R&D Technical Report W178. Author: P.Besley.

TAW, 2002. Technical Report Wave Run-up and Wave Overtopping at Dikes.

TAW, Technical Advisory Committee on Flood Defences. Author: J.W. van der

Meer

EAK, 2002. Ansätz für die Bemessung von Küstenschutzwerken. Chapter 4 in

Die Kuste, Archive for Research and Technology on the North Sea and Baltic

Coast. Empfelungen für Küstenschuzxwerke.

EurOtop Manual

ii Preface

Why is this Manual needed?

This Overtopping Manual gives guidance on analysis and/or prediction of wave

overtopping for flood defences attacked by wave action. It is primarily, but not exclusively,

intended to assist government, agencies, businesses and specialist advisors &

consultants concerned with reducing flood risk. Methods and guidance described in the

manual may also be helpful to designers or operators of breakwaters, reclamations, or

inland lakes or reservoirs

Developments close to the shoreline (coastal, estuarial or lakefront) may be exposed to

significant flood risk yet are often highly valued. Flood risks are anticipated to increase in

the future driven by projected increases of sea levels, more intense rainfall, and stronger

wind speeds. Levels of flood protection for housing, businesses or infrastructure are

inherently variable. In the Netherlands, where two-thirds of the country is below storm

surge level, large rural areas may presently (2007) be defended to a return period of

1:10,000 years, with less densely populated areas protected to 1:4,000 years. In the UK,

where low-lying areas are much smaller, new residential developments are required to be

defended to 1:200 year return.

Understanding future changes in flood risk from waves overtopping seawalls or other

structures is a key requirement for effective management of coastal defences.

Occurrences of economic damage or loss of life due to the hazardous nature of wave

overtopping are more likely, and coastal managers and users are more aware of health

and safety risks. Seawalls range from simple earth banks through to vertical concrete

walls and more complex composite structures. Each of these require different methods to

assess overtopping.

Reduction of overtopping risk is therefore a key requirement for the design, management

and adaptation of coastal structures, particularly as existing coastal infrastructure is

assessed for future conditions. There are also needs to warn or safeguard individuals

potentially to overtopping waves on coastal defences or seaside promenades, particularly

as recent deaths in the UK suggest significant lack of awareness of potential dangers.

Guidance on wave run-up and overtopping have been provided by previous manuals in

UK, Netherlands and Germany including the EA Overtopping Manual edited by Besley

(1999); the TAW Technical Report on Wave run up and wave overtopping at dikes by van

der Meer (2002); and the German Die Küste EAK (2002). Significant new information has

now been obtained from the EC CLASH project collecting data from several nations, and

further advances from national research projects. This Manual takes account of this new

information and advances in current practice. In so doing, this manual will extend and/or

revise advice on wave overtopping predictions given in the CIRIA / CUR Rock Manual, the

Revetment Manual by McConnell (1998), British Standard BS6349, the US Coastal

Engineering Manual, and ISO TC98.

The Manual and Calculation Tool

The Overtopping Manual incorporates new techniques to predict wave overtopping at

seawalls, flood embankments, breakwaters and other shoreline structures. The manual

includes case studies and example calculations. The manual has been intended to assist

coastal engineers analyse overtopping performance of most types of sea defence found

around Europe. The methods in the manual can be used for current performance

assessments and for longer-term design calculations. The manual defines types of

structure, provides definitions for parameters, and gives guidance on how results should

EurOtop Manual

iii

be interpreted. A chapter on hazards gives guidance on tolerable discharges and

overtopping processes. Further discussion identifies the different methods available for

assessing overtopping, such as empirical, physical and numerical techniques.

In parallel with this manual, an online Calculation Tool has been developed to assist the

user through a series of steps to establish overtopping predictions for: embankments and

dikes; rubble mound structures; and vertical structures. By selecting an indicative

structure type and key structural features, and by adding the dimensions of the geometric

and hydraulic parameters, the mean overtopping discharge will be calculated. Where

possible additional results for overtopping volumes, flow velocities and depths, and other

pertinent results will be given.

Intended use

The manual has been intended to assist engineers who are already aware of the general

principles and methods of coastal engineering. The manual uses methods and data from

research studies around Europe and overseas so readers are expected to be familiar with

wave and response parameters and the use of empirical equations for prediction. Users

may be concerned with existing defences, or considering possible rehabilitation or

new-build.

This manual is not, however, intended to cover many other aspects of the analysis,

design, construction or management of sea defences for which other manuals and

methods already exist, see for example the CIRIA / CUR / CETMEF Rock Manual (2007),

the Beach Management Manual by Brampton et al (2002) and TAW guidelines in the

Netherlands on design of sea, river and lake dikes.

What next?

It is clear that increased attention to flood risk reduction, and to wave overtopping in

particular, have increased interest and research in this area. This Manual is, therefore,

not expected to be the ‘last word’ on the subject, indeed even whilst preparing this

version, it was expected that there will be later revisions. At the time of writing this

preface (August 2007), we anticipate that there may be sufficient new research results

available to justify a further small revision of the Manual in the summer or autumn of 2008.

The Authors and Steering Committee

August 2007

EurOtop Manual

v

1.1 Background 1

1.1.1 Previous and related manuals 1

1.1.2 Sources of material and contributing projects 1

1.2 Use of this manual 1

1.3 Principal types of structures 2

1.4 Definitions of key parameters and principal responses 3

1.4.1 Wave height 3

1.4.2 Wave period 4

1.4.3 Wave steepness and Breaker parameter 4

1.4.4 Parameter h* 6

1.4.5 Toe of structure 6

1.4.6 Foreshore 6

1.4.7 Slope 7

1.4.8 Berm 7

1.4.9 Crest freeboard and armour freeboard and width 7

1.4.10 Permeability, porosity and roughness 9

1.4.11 Wave run-up height 10

1.4.12 Wave overtopping discharge 10

1.4.13 Wave overtopping volumes 11

1.5 Probability levels and uncertainties 12

1.5.1 Definitions 12

1.5.2 Background 12

1.5.3 Parameter uncertainty 14

1.5.4 Model uncertainty 14

1.5.5 Methodology and output 15

2.1 Introduction 17

2.2 Water levels, tides, surges and sea level changes 17

2.2.1 Mean sea level 17

2.2.2 Astronomical tide 17

2.2.3 Surges related to extreme weather conditions 18

2.2.4 High river discharges 19

2.2.5 Effect on crest levels 19

2.3 Wave conditions 20

2.4 Wave conditions at depth-limited situations 22

2.5 Currents 25

2.6 Application of design conditions 25

2.7 Uncertainties in inputs 26

3.1 Introduction 27

3.1.1 Wave overtopping processes and hazards 27

3.1.2 Types of overtopping 28

3.1.3 Return periods 29

3.2 Tolerable mean discharges 30

3.3 Tolerable maximum volumes and velocities 34

EurOtop Manual

vi 3.3.1 Overtopping volumes 34

3.3.2 Overtopping velocities 34

3.3.3 Overtopping loads and overtopping simulator 35

3.4 Effects of debris and sediment in overtopping flows 37

4.1 Introduction 39

4.2 Empirical models, including comparison of structures 39

4.2.1 Mean overtopping discharge 39

4.2.2 Overtopping volumes and Vmax 43

4.2.3 Wave transmission by wave overtopping 45

4.4 Neural network tools 53

4.5 Use of CLASH database 58

4.6 Outline of numerical model types 60

4.6.1 Navier-Stokes models 61

4.6.2 Nonlinear shallow water equation models 61

4.7 Physical modelling 62

4.8 Model and Scale effects 63

4.8.1 Scale effects 63

4.8.2 Model and measurement effects 63

4.8.3 Methodology 63

4.9 Uncertainties in predictions 65

4.9.1 Empirical Models 65

4.9.2 Neural Network 65

4.9.3 CLASH database 65

4.10 Guidance on use of methods 65

5.1 Introduction 67

5.2 Wave run-up 68

5.2.1 History of the 2% value for wave run-up 74

5.3 Wave overtopping discharges 74

5.3.1 Simple slopes 74

5.3.2 Effect of roughness 82

5.3.3 Effect of oblique waves 86

5.3.4 Composite slopes and berms 89

5.3.5 Effect of wave walls 93

5.4 Overtopping volumes 95

5.5 Overtopping flow velocities and overtopping flow depth 96

5.5.1 Seaward Slope 97

5.5.2 Dike Crest 99

5.5.3 Landward Slope 102

5.6 Scale effects for dikes 105

5.7 Uncertainties 105

6.1 Introduction 107

6.2 Wave run-up and run-down levels, number of overtopping waves 108

6.3 Overtopping discharges 113

6.3.1 Simple armoured slopes 113

6.3.2 Effect of armoured crest berm 115

6.3.3 Effect of oblique waves 116

6.3.4 Composite slopes and berms, including berm breakwaters 116

EurOtop Manual

vii

6.3.5 Effect of wave walls 119

6.3.6 Scale and model effect corrections 120

6.4 Overtopping volumes per wave 121

6.5 Overtopping velocities and spatial distribution 122

6.6 Overtopping of shingle beaches 124

6.7 Uncertainties 124

7.1 Introduction 127

7.2 Wave processes at walls 129

7.2.1 Overview 129

7.2.2 Overtopping regime discrimination – plain vertical walls 131

7.2.3 Overtopping regime discrimination – composite vertical walls 131

7.3 Mean overtopping discharges for vertical and battered walls 132

7.3.1 Plain vertical walls 132

7.3.2 Battered walls 137

7.3.3 Composite vertical walls 138

7.3.4 Effect of oblique waves 140

7.3.5 Effect of bullnose and recurve walls 142

7.3.6 Effect of wind 145

7.3.7 Scale and model effect corrections 146

7.4 Overtopping volumes 148

7.4.1 Introduction 148

7.4.2 Overtopping volumes at plain vertical walls 148

7.4.3 Overtopping volumes at composite (bermed) structures 150

7.4.4 Overtopping volumes at plain vertical walls under oblique wave attack

7.4.5 Scale effects for individual overtopping volumes 151

7.5 Overtopping velocities, distributions and down-fall pressures 151

7.5.1 Introduction to post-overtopping processes 151

7.5.2 Overtopping throw speeds 151

7.5.3 Spatial extent of overtopped discharge 152

7.5.4 Pressures resulting from downfalling water mass 153

7.6 Uncertainties 153

EurOtop Manual

viii

Figures

Figure 1.1: Type of breaking on a slope......................................................................... 5

Figure 1.2: Spilling waves on a beach; ξm-1,0 < 0.2 ......................................................... 5

Figure 1.3: Plunging waves; ξm-1,0 < 2.0 ......................................................................... 6

Figure 1.4: Crest freeboard different from armour freeboard ......................................... 8

Figure 1.5: Crest freeboard ignores a permeable layer if no crest element is present... 8

Figure 1.6: Crest configuration for a vertical wall ........................................................... 9

Figure 1.7: Example of wave overtopping measurements, showing the random

Figure 1.8: Sources of uncertainties............................................................................. 13

Figure 1.9: Gaussian distribution function and variation of parameters ....................... 14

Figure 2.1: Measurements of maximum water levels for more than 100 years and

extrapolation to extreme return periods...................................................... 19

Figure 2.2: Important aspects during calculation or assessment of dike height ........... 20

Figure 2.3: Wave measurements and numerical simulations in the North Sea (19641993), leading to an extreme distribution ................................................... 21

Figure 2.4: Depth-limited significant wave heights for uniform foreshore slopes ......... 23

Figure 2.5: Computed composite Weibull distribution. Hm0 = 3.9 m; foreshore slope

1:40 and water depth h = 7 m .................................................................... 24

Figure 2.6: Encounter probability ................................................................................. 26

Figure 3.1: Overtopping on embankment and promenade seawalls ............................ 29

Figure 3.2: Wave overtopping test on bare clay; result after 6 hours with 10 l/s per m

Figure 3.3: Example wave forces on a secondary wall ................................................ 35

Figure 3.4: Principle of the wave overtopping simulator............................................... 36

Figure 3.5: The wave overtopping simulator discharging a large overtopping volume

on the inner slope of a dike ........................................................................ 36

Figure 4.1: Comparison of wave overtopping formulae for various kind of structures.. 42

Figure 4.2: Comparison of wave overtopping as function of slope angle ..................... 42

Figure 4.3: Various distributions on a Rayleigh scale graph. A straight line (b = 2) is

a Rayleigh distribution................................................................................ 43

Figure 4.4: Relationship between mean discharge and maximum overtopping

volume in one wave for smooth, rubble mound and vertical structures for

wave heights of 1 m and 2.5 m .................................................................. 45

Figure 4.5: Wave transmission for a gentle smooth structure of 1:4 and for different

wave steepness.......................................................................................... 46

Figure 4.6: Wave overtopping for a gentle smooth structure of 1:4 and for different

wave steepness.......................................................................................... 46

Figure 4.7: Wave transmission versus wave overtopping for a smooth 1:4 slope and

a wave height of Hm0 = 3 m. ....................................................................... 47

Figure 4.8: Wave transmission versus wave overtopping discharge for a rubble

mound structure, cotα = 1.5; 6-10 ton rock, B = 4.5 m and Hm0 = 3 m ..... 48

Figure 4.9: Comparison of wave overtopping and transmission for a vertical, rubble

mound and smooth structure...................................................................... 49

Figure 4.10: Wave overtopping and transmission at breakwater IJmuiden, the

Figure 4.11: Example cross-section of a dike................................................................. 50

Figure 4.12: Input of geometry by x-y coordinates and choice of top material ............... 51

Figure 4.13: Input file...................................................................................................... 51

Figure 4.14: Output of PC-OVERTOPPING......................................................................... 52

Figure 4.15: Check on 2%-runup level ........................................................................... 52

Figure 4.16: Check on mean overtopping discharge...................................................... 52

Figure 4.17: Configuration of the neural network for wave overtopping ......................... 54

Figure 4.18: Overall view of possible structure configurations for the neural network ... 56

Figure 4.19: Example cross-section with parameters for application of neural network. 57

EurOtop Manual

ix Figure 4.20: Results of a trend calculation .....................................................................57

Figure 4.21: Overtopping for large wave return walls; first selection ..............................59

Figure 4.22: Overtopping for large wave return walls; second selection with more

Figure 4.23: Overtopping for a wave return wall with so = 0.04, seaward angle of 45˚,

a width of 2 m and a crest height of Rc = 3 m. For Hm0 toe = 3 m the

overtopping can be estimated from Rc/Hm0 toe = 1.......................................60

Figure 5.1: Wave run-up and wave overtopping for coastal dikes and embankment

seawalls: definition sketch. See Section 1.4 for definitions. ......................67

Figure 5.2: Main calculation procedure for coastal dikes and embankment seawalls ..68

Figure 5.3: Definition of the wave run-up height Ru2% on a smooth impermeable

Figure 5.4: Relative Wave run-up height Ru2%/Hm0 as a function of the breaker

parameter ξm-1,0, for smooth straight slopes ...............................................70

Figure 5.5: Relative Wave run-up height Ru2%/Hm0 as a function of the wave

steepness for smooth straight slopes .........................................................70

Figure 5.6: Wave run-up for smooth and straight slopes..............................................72

Figure 5.7: Wave run-up for deterministic and probabilistic design ..............................73

Figure 5.8: Wave overtopping as a function of the wave steepness Hm0/L0 and the

Figure 5.9: Wave overtopping data for breaking waves and overtopping Equation

5.8 with 5% under and upper exceedance limits ........................................76

Figure 5.10: Wave overtopping data for non-breaking waves and overtopping

Equation 5.9 with 5% under and upper exceedance limits .........................77

Figure 5.11: Wave overtopping for breaking waves – Comparison of formulae for

design and safety assessment and probabilistic calculations.....................78

Figure 5.12: Wave overtopping for non-breaking waves – Comparison of formulae for

design and safety assessment and probabilistic calculations.....................78

Figure 5.13: Dimensionless overtopping discharge for zero freeboard (Schüttrumpf,

Figure 5.14: Wave overtopping and overflow for positive, zero and negative freeboard 81

Figure 5.15: Dike covered by grass (photo: Schüttrumpf) ..............................................82

Figure 5.16: Dike covered by asphalt (photo: Schüttrumpf)............................................82

Figure 5.17: Dike covered by natural bloc revetment (photo: Schüttrumpf)....................83

Figure 5.18: Influence factor for grass surface ...............................................................83

Figure 5.19: Example for roughness elements (photo: Schüttrumpf) .............................84

Figure 5.20: Dimensions of roughness elements............................................................85

Figure 5.21: Performance of roughness elements showing the degree of turbulence....86

Figure 5.22: Definition of angle of wave attack β ............................................................87

Figure 5.23: Short crested waves resulting in wave run-up and wave overtopping

(photo: Zitscher) .........................................................................................88

Figure 5.24: Influence factor γβ for oblique wave attack and short crested waves,

measured data are for wave run-up............................................................89

Figure 5.25: Determination of the average slope (1st estimate) ......................................90

Figure 5.26: Determination of the average slope (2nd estimate) .....................................90

Figure 5.27: Determination of the characteristic berm length LBerm.................................91

Figure 5.28: Typical berms (photo: Schüttrumpf)............................................................91

Figure 5.29: Influence of the berm depth on factor rdh ....................................................93

Figure 5.30: Sea dike with vertical crest wall (photo: Hofstede) .....................................93

Figure 5.31: Influence of a wave wall on wave overtopping (photo: Schüttrumpf)..........94

Figure 5.32: Example probability distribution for wave overtopping volumes per wave..96

Figure 5.33: Wave overtopping on the landward side of a seadike (photo: Zitscher) .....97

Figure 5.34: Definition sketch for layer thickness and wave run-up velocities on the

seaward slope ............................................................................................98

EurOtop Manual

x Figure 5.35: Wave run-up velocity and wave run-up flow depth on the seaward slope

Figure 5.36: Sequence showing the transition of overtopping flow on a dike crest

(Large Wave Flume, Hannover) ............................................................... 100

Figure 5.37: Definition sketch for overtopping flow parameters on the dike crest ........ 101

Figure 5.38: Overtopping flow velocity data compared to the overtopping flow velocity

Figure 5.39: Sensitivity analysis for the dike crest (left side: influence of overtopping

flow depth on overtopping flow velocity; right side: influence of bottom

friction on overtopping flow velocity) ........................................................ 102

Figure 5.40: Overtopping flow on the landward slope (Large Wave Flume, Hannover)

(photo: Schüttrumpf)................................................................................. 103

Figure 5.41: Definition of overtopping flow parameters on the landward slope............ 104

Figure 5.42: Sensitivity Analysis for Overtopping flow velocities and related

overtopping flow depths – Influence of the landward slope - ................... 104

Figure 5.43: Wave overtopping over sea dikes, including results from uncertainty

calculations .............................................................................................. 106

Figure 6.1 Armoured structures................................................................................. 108

Figure 6.2: Relative run-up on straight rock slopes with permeable and impermeable

core, compared to smooth impermeable slopes ...................................... 109

Figure 6.3: Run-up level and location for overtopping differ....................................... 111

Figure 6.4: Percentage of overtopping waves for rubble mound breakwaters as a

function of relative (armour) crest height and armour size (Rc ≤ Ac) ........ 112

Figure 6.5: Relative 2% run-down on straight rock slopes with impermeable core

(imp), permeable core (perm) and homogeneous structure (hom) .......... 113

Figure 6.6: Mean overtopping discharge for 1:1.5 smooth and rubble mound slopes 115

Figure 6.7 Icelandic Berm breakwater....................................................................... 117

Figure 6.8: Conventional reshaping berm breakwater................................................ 117

Figure 6.9: Non-reshaping Icelandic berm breakwater with various classes of big

Figure 6.10: Proposed adjustment factor applied to data from two field sites

(Zeebrugge 1:1.4 rubble mound breakwater, and Ostia 1:4 rubble slope)121

Figure 6.11: Definition of y for various cross-sections.................................................. 123

Figure 6.12: Definition of x- and y-coordinate for spatial distribution............................ 123

Figure 7.1: Examples of vertical breakwaters: (left) modern concrete caisson and

(right) older structure constructed from concrete blocks .......................... 127

Figure 7.2: Examples of vertical seawalls: (left) modern concrete wall and (right)

older stone blockwork wall ....................................................................... 127

Figure 7.3: A non-impulsive (pulsating) wave condition at a vertical wall, resulting in

non-impulsive (or “green water”) overtopping .......................................... 130

Figure 7.4: An impulsive (breaking) wave at a vertical wall, resulting in an impulsive

(violent) overtopping condition ................................................................. 130

Figure 7.5: A broken wave at a vertical wall, resulting in a broken wave overtopping

Figure 7.6: Definition sketch for assessment of overtopping at plain vertical walls.... 131

Figure 7.7: Definition sketch for assessment of overtopping at composite vertical

Figure 7.8: Mean overtopping at a plain vertical wall under non-impulsive conditions

(Equations 7.3 and 7.4) ............................................................................ 133

Figure 7.9: Dimensionless overtopping discharge for zero freeboard (Smid, 2001) .. 134

Figure 7.10: Mean overtopping at a plain vertical wall under impulsive conditions

(Equations 7.6 and 7.7) ............................................................................ 135

Figure 7.11: Mean overtopping discharge for lowest h* Rc / Hm0 (for broken waves

only arriving at wall) with submerged toe (hs > 0). For 0.02 < h* Rc / Hm0

< 0.03, overtopping response is ill-defined – lines for both impulsive

EurOtop Manual

xi conditions (extrapolated to lower h* Rc / Hm0) and broken wave only

conditions (extrapolated to higher h* Rc / Hm0) are shown as dashed lines

over this region .........................................................................................136

Figure 7.12: Mean overtopping discharge with emergent toe (hs < 0) ..........................137

Figure 7.13: Battered walls: typical cross-section (left), and Admiralty Breakwater,

Alderney Channel Islands (right, courtesy G.Müller) ................................138

Figure 7.14: Overtopping for a 10:1 and 5:1 battered walls..........................................138

Figure 7.15: Overtopping for composite vertical walls ..................................................140

Figure 7.16: Overtopping of vertical walls under oblique wave attack..........................141

Figure 7.17: An example of a modern, large vertical breakwater with wave return wall

(left) and cross-section of an older seawall with recurve (right)................142

Figure 7.18: A sequence showing the function of a parapet / wave return wall in

reducing overtopping by redirecting the uprushing water seaward (back

Figure 7.19: Parameter definitions for assessment of overtopping at structures with

parapet / wave return wall ........................................................................143

Figure 7.20: “Decision chart” summarising methodology for tentative guidance. Note

that symbols R0*, k23, m and m* used (only) at intermediate stages of the

procedure are defined in the lowest boxes in the figure. Please refer to

text for further explanation. .......................................................................144

Figure 7.21: Wind adjustment factor fwind plotted over mean overtopping rates qss.......145

Figure 7.22: Large-scale laboratory measurements of mean discharge at 10:1

battered wall under impulsive conditions showing agreement with

prediction line based upon small-scale tests (Equation 7.12)...................147

Figure 7.23: Results from field measurements of mean discharge at Samphire Hoe,

UK, plotted together with Equation 7.13 ...................................................147

Figure 7.24: Predicted and measured maximum individual overtopping volume –

small- and large-scale tests (Pearson et al., 2002) ..................................149

Figure 7.25 Speed of upward projection of overtopping jet past structure crest plotted

with “impulsiveness parameter” h* (after Bruce et al., 2002) ....................152

Figure 7.26 Landward distribution of overtopping discharge under impulsive

conditions. Curves show proportion of total overtopping discharge which

has landed within a particular distance shoreward of seaward crest........153

EurOtop Manual

xii

Tables

Table 2.1: Values of dimensionless wave heights for some values of Htr/Hrms............ 25

Table 3.1: Hazard Type............................................................................................... 30

Table 3.2: Limits for overtopping for pedestrians ........................................................ 31

Table 3.3: Limits for overtopping for vehicles.............................................................. 32

Table 3.4: Limits for overtopping for property behind the defence .............................. 32

Table 3.5: Limits for overtopping for damage to the defence crest or rear slope ........ 33

Table 4.1: Example input file for neural network with first 6 calculations .................... 55

Table 4.2: Output file of neural network with confidence limits ................................... 55

Table 4.3: Scale effects and critical limits ................................................................... 64

Table 5.1: Owen’s coefficients for simple slopes ........................................................ 79

Table 5.2: Surface roughness factors for typical elements ......................................... 85

Table 5.3: Characteristic values for parameter c2 (TMA-spectra) ............................... 98

Table 5.4: Characteristic Values for Parameter a0* (TMA-spectra) ............................. 99

Table 6.1: Main calculation procedure for armoured rubble slopes and mounds...... 107

Table 6.2: Values for roughness factor γf for permeable rubble mound structures

with slope of 1:1.5. Values in italics are estimated/extrapolated ............. 115

Table 7.1: Summary of principal calculation procedures for vertical structures ........ 129

Table 7.2: Summary of prediction formulae for individual overtopping volumes

under oblique wave attack. Oblique cases valid for 0.2 < h* Rc / Hm0 <

0.65. For 0.07 < h* Rc / Hm0 < 0.2, the β = 00 formulae should be used for

Table 7.3: Probabilistic and deterministic design parameters for vertical and

battered walls ........................................................................................... 154

EurOtop Manual

xiii

EurOtop Manual

1.1 Background

This manual describes methods to predict wave overtopping of sea defence and related

coastal or shoreline structures. It recommends approaches for calculating mean

overtopping discharges, maximum overtopping volumes and the proportion of waves

overtopping a seawall. The manual will help engineers to establish limiting tolerable

discharges for design wave conditions, and then use the prediction methods to confirm

that these discharges are not exceeded.

1.1.1 Previous and related manuals

This manual is developed from, at least in part, three manuals: the (UK) Environment

Agency Manual on Overtopping edited by Besley (1999); the (Netherlands) TAW

Technical Report on Wave run-up and wave overtopping at dikes, edited by Van der Meer

(2002); and the German Die Küste EAK (2002) edited by Erchinger. The new combined

manual is intended to revise, extend and develop the parts of those manuals discussing

wave run-up and overtopping.

In so doing, this manual will also extend and/or revise advice on wave overtopping

predictions given in the CIRIA / CUR Rock Manual, the Revetment Manual by McConnell

(1998), British Standard BS6349, the US Coastal Engineering Manual, and ISO TC98.

1.1.2 Sources of material and contributing projects

Beyond the earlier manuals discussed in section 1.3, new methods and data have been

derived from a number of European and national research programmes. The main new

contributions to this manual have been derived from OPTICREST; PROVERBS; CLASH &

SHADOW, VOWS and Big-VOWS and partly ComCoast. Everything given in this manual

is supported by research papers and manuals described in the bibliography.

1.2 Use of this manual

The manual has been intended to assist an engineer analyse the overtopping

performance of any type of sea defence or related shoreline structure found around

Europe. The manual uses the results of research studies around Europe and further

overseas to predict wave overtopping discharges, number of overtopping waves, and the

distributions of overtopping volumes. It is envisaged that methods described here may be

used for current performance assessments, and for longer-term design calculations.

Users may be concerned with existing defences, or considering possible rehabilitation or

new-build.

The analysis methods described in this manual are primarily based upon a deterministic

approach in which overtopping discharges (or other responses) are calculated for wave

and water level conditions representing a given return period. All of the design equations

require data on water levels and wave conditions at the toe of the defence structure. The

input water level should include a tidal and, if appropriate, a surge component. Surges

are usually comprised of components including wind set-up and barometric pressure.

Input wave conditions should take account of nearshore wave transformations, including

breaking. Methods of calculating depth-limited wave conditions are outlined in Chapter 2.

All of the prediction methods given in this report have intrinsic limitations to their accuracy.

For empirical equations derived from physical model data, account should be taken of the

inherent scatter. This scatter, or reliability of the equations, has been described where

possible or available and often equations for deterministic use are given where some

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safety has been taken into account. Still it can be concluded that overtopping rates

calculated by empirically derived equations, should only be regarded as being within, at

best, a factor of 1 - 3 of the actual overtopping rate. The largest deviations will be found

for small overtopping discharges.

As however many practical structures depart (at least in part) from the idealised versions

tested in hydraulics laboratories, and it is known that overtopping rates may be very

sensitive to small variations in structure geometry, local bathymetry and wave climate,

empirical methods based upon model tests conducted on generic structural types, such as

vertical walls, armoured slopes etc may lead to large differences in overtopping

performance. Methods presented here will not predict overtopping performance with the

same degree of accuracy as structure-specific model tests.

This manual is not however intended to cover many other aspects of the analysis, design,

construction or management of sea defences for which other manuals and methods

already exist, see for example CIRIA / CUR (1991), BSI (1991), Simm et al. (1996),

Brampton et al. (2002) and TAW guidelines in the Netherlands on design of sea, river and

lake dikes. The manual has been kept deliberately concise in order to maintain clarity and

brevity. For the interested reader a full set of references is given so that the reasoning

behind the development of the recommended methods can be followed.

1.3 Principal types of structures

Wave overtopping is of principal concern for structures constructed primarily to defend

against flooding: often termed sea defence. Somewhat similar structures may also be

used to provide protection against coastal erosion: sometimes termed coast protection.

Other structures may be built to protect areas of water for ship navigation or mooring:

ports, harbours or marinas; these are often formed as breakwaters or moles. Whilst some

of these types of structures may be detached from the shoreline, sometimes termed

offshore, nearshore or detached, most of the structures used for sea defence form a part

of the shoreline.

This manual is primarily concerned with the three principal types of sea defence

structures: sloping sea dikes and embankment seawalls; armoured rubble slopes and

mounds; and vertical, battered or steep walls.

Historically, sloping dikes have been the most widely used option for sea defences along

the coasts of the Netherlands, Denmark, Germany and many parts of the UK. Dikes or

embankment seawalls have been built along many Dutch, Danish or German coastlines

protecting the land behind from flooding, and sometimes providing additional amenity

value. Similar such structures in UK may alternatively be formed by clay materials or from

a vegetated shingle ridge, in both instances allowing the side slopes to be steeper. All

such embankments will need some degree of protection against direct wave erosion,

generally using a revetment facing on the seaward side. Revetment facing may take

many forms, but may commonly include closely-fitted concrete blockwork, cast in-situ

concrete slabs, or asphaltic materials. Embankment or dike structures are generally most

common along rural frontages.

A second type of coastal structure consists of a mound or layers of quarried rock fill,

protected by rock or concrete armour units. The outer armour layer is designed to resist

wave action without significant displacement of armour units. Under-layers of quarry or

crushed rock support the armour and separate it from finer material in the embankment or

mound. These porous and sloping layers dissipate a proportion of the incident wave

energy in breaking and friction. Simplified forms of rubble mounds may be used for rubble

seawalls or protection to vertical walls or revetments. Rubble mound revetments may

also be used to protect embankments formed from relict sand dunes or shingle ridges.

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Rubble mound structures tend to be more common in areas where harder rock is

available.

Along urban frontages, especially close to ports, erosion or flooding defence structures

may include vertical (or battered / steep) walls. Such walls may be composed of stone or

concrete blocks, mass concrete, or sheet steel piles. Typical vertical seawall structures

may also act as retaining walls to material behind. Shaped and recurved wave return

walls may be formed as walls in their own right, or smaller versions may be included in

sloping structures. Some coastal structures are relatively impermeable to wave action.

These include seawalls formed from blockwork or mass concrete, with vertical, near

vertical, or steeply sloping faces. Such structures may be liable to intense local wave

impact pressures, may overtop suddenly and severely, and will reflect much of the

incident wave energy. Reflected waves cause additional wave disturbance and/or may

initiate or accelerate local bed scour.

1.4 Definitions of key parameters and principal responses

Overtopping discharge occurs because of waves running up the face of a seawall. If

wave run-up levels are high enough water will reach and pass over the crest of the wall.

This defines the ‘green water’ overtopping case where a continuous sheet of water passes

over the crest. In cases where the structure is vertical, the wave may impact against the

wall and send a vertical plume of water over the crest.

A second form of overtopping occurs when waves break on the seaward face of the

structure and produce significant volumes of splash. These droplets may then be carried

over the wall either under their own momentum or as a consequence of an onshore wind.

Another less important method by which water may be carried over the crest is in the form

of spray generated by the action of wind on the wave crests immediately offshore of the

wall. Even with strong wind the volume is not large and this spray will not contribute to

any significant overtopping volume.

Overtopping rates predicted by the various empirical formulae described within this report

will include green water discharges and splash, since both these parameters were

recorded during the model tests on which the prediction methods are based. The effect of

wind on this type of discharge will not have been modelled. Model tests suggest that

onshore winds have little effect on large green water events, however they may increase

discharges under 1 l/s/m. Under these conditions, the water overtopping the structure is

mainly spray and therefore the wind is strong enough to blow water droplets inshore.

In the list of symbols, short definitions of the parameters used have been included. Some

definitions are so important that they are explained separately in this section as key

parameters. The definitions and validity limits are specifically concerned with application

of the given formulae. In this way, a structure section with a slope of 1:12 is not

considered as a real slope (too gentle) and it is not a real berm too (too steep). In such a

situation, wave run-up and overtopping can only be calculated by interpolation. For

example, for a section with a slope of 1:12, interpolation can be made between a slope of

1:8 (mildest slope) and a 1:15 berm (steepest berm).

1.4.1 Wave height

The wave height used in the wave run-up and overtopping formulae is the incident

significant wave height Hm0 at the toe of the structure, called the spectral wave height,

Hm0 = 4(m0)½. Another definition of significant wave height is the average of the highest

third of the waves, H1/3. This wave height is, in principle, not used in this manual, unless

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formulae were derived on basis of it. In deep water, both definitions produce almost the

same value, but situations in shallow water can lead to differences of 10-15%.

In many cases, a foreshore is present on which waves can break and by which the

significant wave height is reduced. There are models that in a relatively simple way can

predict the reduction in energy from breaking of waves and thereby the accompanying

wave height at the toe of the structure. The wave height must be calculated over the total

spectrum including any long-wave energy present.

Based on the spectral significant wave height, it is reasonably simple to calculate a wave

height distribution and accompanying significant wave height H1/3 using the method of

Battjes and Groenendijk (2000).

1.4.2 Wave period

Various wave periods can be defined for a wave spectrum or wave record. Conventional

wave periods are the peak period Tp (the period that gives the peak of the spectrum), the

average period Tm (calculated from the spectrum or from the wave record) and the

significant period T1/3 (the average of the highest 1/3 of the waves). The relationship

Tp/Tm usually lies between 1.1 and 1.25, and Tp and T1/3 are almost identical.

The wave period used for some wave run-up and overtopping formulae is the spectral

period Tm-1.0 (= m-1/m0). This period gives more weight to the longer periods in the

spectrum than an average period and, independent of the type of spectrum, gives similar

wave run-up or overtopping for the same values of Tm-1,0 and the same wave heights. In

this way, wave run-up and overtopping can be easily determined for double-peaked and

'flattened' spectra, without the need for other difficult procedures. Vertical and steep

seawalls often use the Tm0,1 or Tm wave period.

In the case of a uniform (single peaked) spectrum there is a fixed relationship between the

spectral period Tm-1.0 and the peak period. In this report a conversion factor

(Tp = 1.1 Tm-1.0) is given for the case where the peak period is known or has been

determined, but not the spectral period.

1.4.3 Wave steepness and Breaker parameter

Wave steepness is defined as the ratio of wave height to wavelength (e.g. s0 = Hm0/L0).

This will tell us something about the wave’s history and characteristics. Generally a

steepness of s0 = 0.01 indicates a typical swell sea and a steepness of s0 = 0.04 to 0.06 a

typical wind sea. Swell seas will often be associated with long period waves, where it is

the period that becomes the main parameter that affects overtopping.

But also wind seas may became seas with low wave steepness if the waves break on a

gentle foreshore. By wave breaking the wave period does not change much, but the wave

height decreases. This leads to a lower wave steepness. A low wave steepness on

relatively deep water means swell waves, but for depth limited locations it often means

broken waves on a (gentle) foreshore.

The breaker parameter, surf similarity or Iribarren number is defined as

ξm-1,0 = tanα/(Hm0/Lm-1,0)½, where α is the slope of the front face of the structure and Lm-1,0

being the deep water wave length gT2m-1,0/2π. The combination of structure slope and

wave steepness gives a certain type of wave breaking, see Figure 1.1. For ξm-1,0 > 2-3

waves are considered not to be breaking (surging waves), although there may still be

some breaking, and for ξm-1,0 < 2-3 waves are breaking. Waves on a gentle foreshore

break as spilling waves and more than one breaker line can be found on such a foreshore,

see Figure 1.2. Plunging waves break with steep and overhanging fronts and the wave

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tongue will hit the structure or back washing water; an example is shown in Figure 1.3.

The transition between plunging waves and surging waves is known as collapsing. The

wave front becomes almost vertical and the water excursion on the slope (wave run-up +

run down) is often largest for this kind of breaking. Values are given for the majority of the

larger waves in a sea state. Individual waves may still surge for generally plunging

conditions or plunge for generally surging conditions.

Figure 1.1: Type of breaking on a slope

Figure 1.2: Spilling waves on a beach; ξm-1,0 < 0.2

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Figure 1.3: Plunging waves; ξm-1,0 < 2.0

1.4.4 Parameter h*

In order to distinguish between non-impulsive (previously referred to as pulsating) waves

on a vertical structure and impulsive (previously referred to as impacting) waves, the

parameter h* has been defined.

o s s s

h

h h =* 1.1

The parameter describes two ratios together, the wave height and wave length, both

made relative to the local water depth hs. Non-impulsive waves predominate when

h* > 0.3; impulsive waves when h* ≤ 0.3. Formulae for impulsive overtopping on vertical

structures, originally used this h* parameter to some power, both for the dimensionless

wave overtopping and dimensionless crest freeboard.

1.4.5 Toe of structure

In most cases, it is clear where the toe of the structure lies, and that is where the

foreshore meets the front slope of the structure or the toe structure in front of it. For

vertical walls, it will be at the base of the principal wall, or if present, at the rubble mound

toe in front of it. It is possible that a sandy foreshore varies with season and even under

severe wave attack. Toe levels may therefore vary during a storm, with maximum levels

of erosion occurring during the peak of the tidal / surge cycle. It may therefore be

necessary to consider the effects of increased wave heights due to the increase in the toe

depth. The wave height that is always used in wave overtopping calculations is the

incident wave height at the toe.

1.4.6 Foreshore

The foreshore is the section in front of the dike and can be horizontal or up to a maximum

slope of 1:10. The foreshore can be deep, shallow or very shallow. If the water is shallow

or very shallow then shoaling and depth limiting effects will need to be considered so that

the wave height at the toe; or end of the foreshore; can be considered. A foreshore is

defined as having a minimum length of one wavelength Lo. In cases where a foreshore

lies in very shallow depths and is relatively short, then the methods outlined in Section

5.3.4 should be used.

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A precise transition from a shallow to a very shallow foreshore is hard to give. At a

shallow foreshore waves break and the wave height decreases, but the wave spectrum

will retain more or less the shape of the incident wave spectrum. At very shallow

foreshores the spectral shape changes drastically and hardly any peak can be detected

(flat spectrum). As the waves become very small due to breaking many different wave

periods arise.

Generally speaking, the transition between shallow and very shallow foreshores can be

indicated as the situation where the original incident wave height, due to breaking, has

been decreased by 50% or more. The wave height at a structure on a very shallow

foreshore is much smaller than in deep water situations. This means that the wave

steepness (Section 1.4.3) becomes much smaller, too. Consequently, the breaker

parameter, which is used in the formulae for wave run-up and wave overtopping, becomes

much larger. Values of ξ0 = 4 to 10 for the breaker parameter are then possible, where

maximum values for a dike of 1:3 or 1:4 are normally smaller than say ξ0 = 2 or 3.

Another possible way to look at the transition from shallow to very shallow foreshores, is

to consider the breaker parameter. If the value of this parameter exceeds 5-7, or if they

are swell waves, then a very shallow foreshore is present. In this way, no knowledge

about wave heights at deeper water is required to distinguish between shallow and very

shallow foreshores.

1.4.7 Slope

Part of a structure profile is defined as a slope if the slope of that part lies between 1:1

and 1:8. These limits are also valid for an average slope, which is the slope that occurs

when a line is drawn between -1.5 Hm0 and +Ru2% in relation to the still water line and

berms are not included. A continuous slope with a slope between 1:8 and 1:10 can be

calculated in the first instance using the formulae for simple slopes, but the reliability is

less than for steeper slopes. In this case interpolation between a slope 1:8 and a berm

1:15 is not possible.

A structure slope steeper than 1:1, but not vertical, can be considered as a battered wall.

These are treated in Chapter 7 as a complete structure. If it is only a wave wall on top of

gentle sloping dike, it is treated in Chapter 5.

1.4.8 Berm

A berm is part of a structure profile in which the slope varies between horizontal and 1:15.

The position of the berm in relation to the still water line is determined by the depth, dh, the

vertical distance between the middle of the berm and the still water line. The width of a

berm, B, may not be greater than one-quarter of a wavelength, i.e., B < 0.25 Lo. If the

width is greater, then the structure part is considered between that of a berm and a

foreshore, and wave run-up and overtopping can be calculated by interpolation.

Section 5.3.4 gives a more detailed description.

1.4.9 Crest freeboard and armour freeboard and width

The crest height of a structure is defined as the crest freeboard, Rc, and has to be used

for wave overtopping calculations. It is actually the point on the structure where

overtopping water can no longer flow back to the seaside. The height (freeboard) is

related to SWL. For rubble mound structures, it is often the top of a crest element and not

the height of the rubble mound armour.

The armour freeboard, Ac, is the height of a horizontal part of the crest, measured relative

to SWL. The horizontal part of the crest is called Gc. For rubble mound slopes the

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armour freeboard, Ac, may be higher, equal or sometimes lower than the crest freeboard,

Rc, Figure 1.4.

swl

overtopping

measured

behind wall

RcAc

Gc Figure 1.4: Crest freeboard different from armour freeboard

The crest height that must be taken into account during calculations for wave overtopping

for an upper slope with quarry stone, but without a wave wall, is not the upper side of this

quarry stone, Ac. The quarry stone armour layer is itself completely water permeable, so

that the under side must be used instead, see Figure 1.5. In fact, the height of a non or

only slightly water-permeable layer determines the crest freeboard, Rc, in this case for

calculations of wave overtopping.

swl

overtopping

measured

behind wall

RcAc

Gc Figure 1.5: Crest freeboard ignores a permeable layer if no crest element is present

The crest of a dike, especially if a road runs along it, is in many cases not completely

horizontal, but slightly rounded and of a certain width. The crest height at a dike or

embankment, Rc, is defined as the height of the outer crest line (transition from outer

slope to crest). This definition therefore is used for wave run-up and overtopping. In

principle the width of the crest and the height of the middle of the crest have no influence

on calculations for wave overtopping, which also means that Rc = Ac is assumed and that

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Gc = 0. Of course, the width of the crest, if it is very wide, can have an influence on the

actual wave overtopping.

If an impermeable slope or a vertical wall have a horizontal crest with at the rear a wave

wall, then the height of the wave wall determines Rc and the height of the horizontal part

determines Ac, see Figure 1.6.

swl

Rc Ac

GcCREST

Figure 1.6: Crest configuration for a vertical wall

1.4.10 Permeability, porosity and roughness

A smooth structure like a dike or embankment is mostly impermeable for water or waves

and the slope has no, or almost no roughness. Examples are embankments covered with

a placed block revetment, an asphalt or concrete slope and a grass cover on clay.

Roughness on the slope will dissipate wave energy during wave run-up and will therefore

reduce wave overtopping. Roughness is created by irregularly shaped block revetments

or artificial ribs or blocks on a smooth slope.

A rubble mound slope with rock or concrete armour is also rough and in general more

rough than roughness on impermeable dikes or embankments. But there is another

difference, as the permeability and porosity is much larger for a rubble mound structure.

Porosity is defined as the percentage of voids between the units or particles. Actually,

loose materials always have some porosity. For rock and concrete armour the porosity

may range roughly between 30% - 55%. But also sand has a comparable porosity. Still

the behaviour of waves on a sand beach or a rubble mound slope is different.

This difference is caused by the difference in permeability. The armour of rubble mound

slopes is very permeable and waves will easily penetrate between the armour units and

dissipate energy. But this becomes more difficult for the under layer and certainly for the

core of the structure. Difference is made between “impermeable under layers or core”

and a “permeable core”. In both cases the same armour layer is present, but the structure

and under layers differ.

A rubble mound breakwater often has an under layer of large rock (about one tenth of the

weight of the armour), sometimes a second under layer of smaller rock and then the core

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of still smaller rock. Up-rushing waves can penetrate into the armour layer and will then

sink into the under layers and core. This is called a structure with a “permeable core”.

An embankment can also be covered by an armour layer of rock. The under layer is often

small and thin and placed on a geotextile. Underneath the geotextile sand or clay may be

present, which is impermeable for up-rushing waves. Such an embankment covered with

rock has an “impermeable core”. Run-up and wave overtopping are dependent on the

permeability of the core.

In summary the following types of structures can be described:

Smooth dikes and embankments: smooth and impermeable

Dikes and embankments with rough slopes: some roughness and impermeable

Rock cover on an embankment: rough with impermeable core

Rubble mound breakwater: rough with permeable core

1.4.11 Wave run-up height

The wave run-up height is given by Ru2%. This is the wave run-up level, measured

vertically from the still water line, which is exceeded by 2% of the number of incident

waves. The number of waves exceeding this level is hereby related to the number of

incoming waves and not to the number that run-up.

A very thin water layer in a run-up tongue cannot be measured accurately. In model

studies on smooth slopes the limit is often reached at a water layer thickness of 2 mm.

For prototype waves this means a layer depth of about 2 cm, depending on the scale in

relation to the model study. Very thin layers on a smooth slope can be blown a long way

up the slope by a strong wind, a condition that can also not be simulated in a small scale

model. Running-up water tongues less than 2 cm thickness actually contain very little

water. Therefore it is suggested that the wave run-up level on smooth slopes is

determined by the level at which the water tongue becomes less than 2 cm thick. Thin

layers blown onto the slope are not seen as wave run-up.

Run-up is relevant for smooth slopes and embankments and sometimes for rough slopes

armoured with rock or concrete armour. Wave run-up is not an issue for vertical

structures. The percentage or number of overtopping waves, however, is relevant for

each type of structure.

1.4.12 Wave overtopping discharge

Wave overtopping is the mean discharge per linear meter of width, q, for example in

m3/s/m or in l/s/m. The methods described in this manual calculate all overtopping

discharges in m3/s/m unless otherwise stated; it is, however, often more convenient to

multiply by 1000 and quote the discharge in l/s/m.

In reality, there is no constant discharge over the crest of a structure during overtopping.

The process of wave overtopping is very random in time and volume. The highest waves

will push a large amount of water over the crest in a short period of time, less than a wave

period. Lower waves will not produce any overtopping. An example of wave overtopping

measurements is shown in Figure 1.7. The graphs shows 200 s of measurements. The

lowest graph (flow depths) clearly shows the irregularity of wave overtopping. The upper

graph gives the cumulative overtopping as it was measured in the overtopping tank.

Individual overtopping volumes can be distinguished, unless a few overtopping waves

come in one wave group.

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Figure 1.7: Example of wave overtopping measurements, showing the random behaviour

Still a mean overtopping discharge is widely used as it can easily be measured and also

classified:

q < 0.1 l/s per m: Insignificant with respect to strength of crest and rear of

structure.

q = 1 l/s per m: On crest and inner slopes grass and/or clay may start to

erode.

q = 10 l/s per m: Significant overtopping for dikes and embankments. Some

overtopping for rubble mound breakwaters.

q = 100 l/s per m: Crest and inner slopes of dikes have to be protected by

asphalt or concrete; for rubble mound breakwaters

transmitted waves may be generated.

1.4.13 Wave overtopping volumes

A mean overtopping discharge does not yet describe how many waves will overtop and

how much water will be overtopped in each wave. The volume of water, V, that comes

over the crest of a structure is given in m3 per wave per m width. Generally, most of the

overtopping waves are fairly small, but a small number gives significantly larger

overtopping volumes.

The maximum volume overtopped in a sea state depends on the mean discharge q, on

the storm duration and the percentage of overtopping waves. In this report, a method is

given by which the distribution of overtopping volumes can be calculated for each wave.

A longer storm duration gives more overtopping waves, but statistically, also a larger

maximum volume. Many small overtopping waves (like for river dikes or embankments)

may create the same mean overtopping discharge as a few large waves for rough sea

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conditions. The maximum volume will, however, be much larger for rough sea conditions

with large waves.

1.5 Probability levels and uncertainties

This section will briefly introduce the concept of uncertainties and how it will be dealt with

in this manual. It will start with a basic definition of uncertainty and return period. After

that the various types of uncertainties are explained and more detailed descriptions of

parameters and model uncertainties used in this manual will be described.

1.5.1 Definitions

Uncertainty may be defined as the relative variation in parameters or error in the model

description so that there is no single value describing this parameter but a range of

possible values. Due to the random nature of many of those variables used in coastal

engineering most of the parameters should not be treated deterministically but

stochastically. The latter assumes that a parameter x shows different realisations out of a

range of possible values. Hence, uncertainty may be defined as a statistical distribution of

the parameter. If a normal distribution is assumed here uncertainty may also be given as

relative error, mathematically expressed as the coefficient of variation of a certain

parameter x:

x x x μ

where σx is the standard deviation of the parameter and μx is the mean value of that

parameter. Although this definition may be regarded as imperfect it has some practical

value and is easily applied.

The return period of a parameter is defined as the period of time in which the parameter

occurs again on average. Therefore, it is the inverse of the probability of occurrence of

this parameter. If the return period TR of a certain wave height is given, it means that this

specific wave height will only occur once in TR years on average.

It should be remembered that there will not be exactly TR years between events with a

given return period of TR years. If the events are statistically independent then the

probability that a condition with a return period of TR years will occur within a period of L

years is given by p = 1-(1-1/nTR)nL, where n is the number of events per year, e.g., 2920

storms of three hours duration. Hence, for an event with a return period of 100 years

there is a 1% chance of recurrence in any one year. For a time interval equal to the return

period, p = 1-(1-1/nTr)nTr or p ≈ 1 - 1/e = 0.63. Therefore, there is a 63% chance of

occurrence within the return period. Further information on design events and return

periods can be found in the British Standard Code of practice for Maritime Structures

(BS6349 Part 1 1984 and Part 7 1991) or the PIANC working group 12 report (PIANC,

1992). Also refer to Section 2.6.

1.5.2 Background

Many parameters used in engineering models are uncertain, and so are the models

themselves. The uncertainties of input parameters and models generally fall into certain

categories; as summarised in Figure 1.8.

• Fundamental or statistical uncertainties: elemental, inherent uncertainties, which are

conditioned by random processes of nature and which can not be diminished

(always comprised in measured data)

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• Data uncertainty: measurement errors, inhomogeneity of data, errors during data

handling, non-representative reproduction of measurement due to inadequate

temporal and spatial resolution

• Model uncertainty: coverage of inadequate reproduction of physical processes in

nature

• Human errors: all of the errors during production, abrasion, maintenance as well as

other human mistakes which are not covered by the model. These errors are not

considered in the following, due to the fact that in general they are specific to the

problems and no universal approaches are available.

If Normal or Gaussian Distributions for x are used 68.3% of all values of x are within the

range of μx(1 ± σx), 95.5% of all values within the range of μx ± 2σx and almost all values

(97,7%) within the range of μx± 3σx, see Figure 1.9. Considering uncertainties in a design,

therefore, means that all input parameters are no longer regarded as fixed deterministic

parameters but can be any realisation of the specific parameter. This has two

consequences: Firstly, the parameters have to be checked whether all realisations of this

parameter are really physically sound: E.g., a realisation of a normally distributed wave

height can mathematically become negative which is physically impossible. Secondly,

parameters have to be checked against realisations of other parameters: E.g., a wave of a

certain height can only exist in certain water depths and not all combinations of wave

heights and wave periods can physically exist.

Inherent (Basic)

Uncertainties

Human &

Organisation

Errors (HOE)

Model

Uncertainties

Can be reduced by:

- increased data

- improved quality

of collected data

Can be reduced by:

- increased knowledge

- improved models

Can neither be

- reduced nor

- removed

Empirical and

theoretical model

uncertainties

Statistical

distribution

uncertainties

Can be reduced by:

- improved knowledge

- improved organisation

Environmental

parameters, material

properties of random

nature (example: expected wave height at

certain site in

20 years)

Operators (designers...), organisations,

procedures, environment, equipment and

interfaces between

these sources

Hypothesised / fitted

statistical distributions

of random quantities

(fixed time parameters) and random

processes (variable

time parameters)

Empirical (based on

data) and theoretical

relationships used to

describe physical

processes, input

variables and limit state

equations (LSE)

Main Sources and Types of Uncertainties

Figure 1.8: Sources of uncertainties

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68.3% of all values

95.5% of all values

99.7% of all values

with: μ = mean value

σ = standard deviation

Gaussian Distribution FunctionGaussian Distribution Function

Figure 1.9: Gaussian distribution function and variation of parameters

In designing with uncertainties this means that statistical distributions for most of the

parameters have to be selected extremely carefully. Furthermore, physical relations

between parameters have to be respected. This will be discussed in the subsequent

sections as well.

1.5.3 Parameter uncertainty

The uncertainty of input parameters describes the inaccuracy of these parameters, either

from measurements of those or from their inherent uncertainties. As previously

discussed, this uncertainty will be described using statistical distributions or relative

variation of these parameters. Relative variation for most of the parameters will be taken

from various sources such as: measurement errors observed; expert opinions derived

from questionnaires; errors reported in literature.

Uncertainties of parameters will be discussed in the subsections of each of the following

chapters discussing various methods to predict wave overtopping of coastal structures.

Any physical relations between parameters will be discussed and restrictions for

assessing the uncertainties will be proposed.

1.5.4 Model uncertainty

The model uncertainty is considered as the accuracy, with which a model or method can

describe a physical process or a limit state function. Therefore, the model uncertainty

describes the deviation of the prediction from the measured data due to this method.

Difficulties of this definition arise from the combination of parameter uncertainty and model

uncertainty. Differences between predictions and data observations may result from

either uncertainties of the input parameters or model uncertainty.

Model uncertainties may be described using the same approach than for parameter

uncertainties using a multiplicative approach. This means that

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( )ixfmq ⋅= 1.3

where m is the model factor [-]; q is the overtopping ratio and f(x) is the model used for

prediction of overtopping. The model factor m is assumed to be normally distributed with

a mean value of 1.0 and a coefficient of variation specifically derived for the model.

These model factors may easily reach coefficients of variations up to 30%. It should be

noted that a mean value of m = 1.0 always means that there is no bias in the models

used. Any systematic error needs to be adjusted by the model itself. For example, if

there is an over-prediction of a specific model by 20% the model has to be adjusted to

predict 20% lower results. This concept is followed in all further chapters of this manual

so that from here onwards, the term ‘model uncertainties’ is used to describe the

coefficient of variation σ’, assuming that the mean value is always 1.0. The procedure to

account for the model uncertainties is given in section 4.9.1.

Model uncertainties will be more widely discussed in the subsections of each chapter

describing the models. The subsections will also give details on how the uncertain results

of the specific model may be interpreted.

1.5.5 Methodology and output

All parameter and model uncertainties as discussed in the previous sections are used to

run the models proposed in this manual. Results of all models will again follow statistical

distributions rather than being single deterministic values. Hence, interpretation of these

results is required and recommendations will be given on how to use outputs of the

models.

Key models for overtopping will be calculated using all uncertainties and applying a

Monte-Carlo-simulation (MCS). Statistical distributions of outputs will be classified with

regard to exceedance probabilities such as: very safe, where output is only exceeded by

2% of all results, corresponding to a return period of 50 years which means that the

structure is expected to be overtopped only once during its lifetime of 50 years; safe,

where output is exceeded by 10% of all results, corresponding to a return period of 10

years; medium safe, where output corresponds to mean values plus one standard

deviation; and probabilistic, where output is exceeded by 50% of all results and may be

used for probabilistic calculations.

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2.1 Introduction

This Overtopping Manual has a focus on the aspects of wave run-up and wave

overtopping only. It is not a design manual, giving the whole design process of a

structure. This chapter, therefore, will not provide a guide to the derivation of input

conditions other than to identify the key activities in deriving water level and wave

conditions, and particularly depth-limited wave conditions. It identifies the key parameters

and provides a check-list of key processes and transformations. Comprehensive

references are given to appropriate sources of information. Brief descriptions of methods

are sometimes given, summary details of appropriate tools and models, and cross

references to other manuals.

The main manuals and guidelines, which describe the whole design process of coastal

and inland structures, including water levels and wave conditions are: The Rock Manual

(1991), recently replaced by the updated Rock Manual (2007); The Coastal Engineering

Manual; The British Standards; The German “Die Küste” (2002) and the DELOS Design

Guidelines (2007).

2.2 Water levels, tides, surges and sea level changes

Prediction of water levels is extremely important for prediction of wave run-up levels or

wave overtopping, which are often used to design the required crest level of a flood

defence structure or breakwater. Moreover, in shallow areas the extreme water level

often determines the water depth and thereby the upper limit for wave heights.

Extreme water levels in design or assessment of structures may have the following

components: the mean sea level; the astronomical tide; surges related to (extreme)

weather conditions; and high river discharges

2.2.1 Mean sea level

For coastal waters in open communication with the sea, the mean water level can often

effectively be taken as a site-specific constant, being related to the mean sea level of the

oceans. For safety assessments, not looking further ahead than about 5 years, the actual

mean water level can be taken as a constant. Due to expected global warming, however,

predictions in sea level rise for the next hundred years range roughly from 0.2 m to more

than 1.0 m.

For design of structures, which last a long time after their design and construction phase,

a certain sea level rise has to be included. Sometimes countries prescribe a certain sea

level rise, which has to be taken into account when designing flood defence structures.

Also the return period to include sea level rise may differ, due to the possibility of

modification in future. An earthen dike is easy to increase in height and a predicted sea

level rise for the next 50 years would be sufficient. A dedicated flood defence structure

through a city is not easy to modify or replace. In such a situation a predicted sea level

rise for the next 100 years or more could be considered.

2.2.2 Astronomical tide

The basic driving forces of tidal movements are astronomical and therefore entirely

predictable, which enables accurate prediction of tidal levels (and currents). Around the

UK and North Sea coast, and indeed around much of the world, the largest fluctuations in

water level are caused by astronomical tides. These are caused by the relative rotation of

both the sun and the moon around the earth each day. The differential gravitational

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effects over the surface of the oceans cause tides with well defined periods, principally

semi-diurnal and diurnal. Around the British Isles and along coasts around the North Sea

the semi-diurnal tides are much larger than the diurnal components.

In addition to the tides that result from the earth's rotation, other periodicities are apparent

in the fluctuation of tidal levels. The most obvious is the fortnightly spring-neap cycle,

corresponding to the half period of the lunar cycle.

Further details on the generation of astronomic tides, and their dynamics, can be found in

the Admiralty Manual of Tides in most countries. These give daily predictions of times of

high and low waters at selected locations, such as ports. Also details of calculating the

differences in level between different locations are provided. Unfortunately, in practice,

the prediction of an extreme water level is made much more complicated by the effects of

weather, as discussed below.

2.2.3 Surges related to extreme weather conditions

Generally speaking the difference between the level of highest astronomical tide and, say,

the largest predicted tide in any year is rather small (i.e. a few centimetres). In practice,

this difference is often unimportant, when compared with the differences between

predicted and observed tidal levels due to weather effects.

Extreme high water levels are caused by a combination of high tidal elevations plus a

positive surge, which usually comprise three main components. A barometric effect

caused by a variation in atmospheric pressure from its mean value. A wind set-up; in

shallow seas, such as a the English Channel or the North Sea, a strong wind can cause a

noticeable rise in sea level within a few hours. A dynamic effect due to the amplification of

surge-induced motions caused by the shape of the land (e.g. seiching and funnelling).

A fourth component, wave set-up causes an increase in water levels within the surf zone

at a particular site due to waves breaking as they travel shoreward. Unlike the other three

positive surge components, wave set-up has only an extremely localised effect on water

levels. Wave set-up is implicitly reproduced in the physical model tests on which the

overtopping equations are based. There is, therefore, no requirement to add on an

additional water level increase for wave set-up when calculating overtopping discharges

using the methods reported in this document.

Negative surges are made up of two principal components: a barometric effect caused by

high atmospheric pressures and wind set-down caused by winds blowing offshore. Large

positive surges are more frequent than large negative ones. This is because a depression

causing a positive surge will tend to be more intense and associated with a more severe

wind condition than anticyclones.

Surges in relatively large and shallow areas, like the southern part of the North Sea, play

an important role in estimating extreme water levels. The surges may become several

meters for large return periods. The easiest means of predicting extreme water levels is

to analyse long term water level data from the site in question. However, where no such

data exists, it may be necessary to predict surge levels using theoretical equations and

combine these levels with tidal elevations in order to obtain an estimation of extreme

water levels.

More than 100 years’ of high water level measurements in the Netherlands is shown in

Figure 2.1 along with the extrapolation of the measurements to extreme low exceedance

probabilities, such as 10-4 or only once in 10,000 years.

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Figure 2.1: Measurements of maximum water levels for more than 100 years and extrapolation to

extreme return periods

2.2.4 High river discharges

Coastal flood defences face the sea or a (large) lake, but flood defences are also present

along tidal rivers. Extreme river discharges determine the extreme water levels along

river flood defences. During such an extreme water level, which may take a week or

longer, a storm may generate waves on the river and cause overtopping of the flood

defence. In many cases the required height of a river dike does not only depend on the

extreme water level, but also on the possibility of wave overtopping. It should be noted

that the occurrence of the extreme river discharge, and extreme water level, are

independent of the occurrence of the storm. During high river discharges, only “normal”

storms; occurring every decade; are considered, not the extreme storms.

Where rivers enter the sea both systems for extreme water levels may occur. Extreme

storms may give extreme water levels, but also extreme river discharges. The effect of

extreme storms and surges disappear farther upstream. Joint probabilistic calculations of

both phenomena may give the right extreme water levels for design or safety assessment.

2.2.5 Effect on crest levels

During design or safety assessment of a dike, the crest height does not just depend on

wave run-up or wave overtopping. Account must also be taken of a reference level, local

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sudden gusts and oscillations (leading to a corrected water level), settlement and an

increase of the water level due to sea level rise.

Figure 2.2: Important aspects during calculation or assessment of dike height

The structure height of a dike in the Netherlands is composed of the following

contributions; see also the Guidelines for Sea and Lake Dikes [TAW, 1999-2]:

a) the reference level with a probability of being exceeded corresponding to the legal

standard (in the Netherlands this is a return period between 1,250 and 10,000

years;

b) the sea level rise or lake level increase during the design period;

c) the expected local ground subsidence during the design period;

d) an extra due to squalls, gusts, seiches and other local wind conditions;

e) the expected decrease in crest height due to settlement of the dike body and the

foundation soils during the design period;

f) the wave run-up height and the wave overtopping height.

Contributions (a) to (d) cannot be influenced, whereas contribution (e) can be influenced.

Contribution (f) also depends on the outer slope, which can consist of various materials,

such as an asphalt layer, a cement-concrete dike covering (stone setting) or grass on a

clay layer. A combination of these types is also possible. Slopes are not always straight,

and the upper and lower sections may have different slopes and also a berm may be

applied. The design of a covering layer is not dealt with in this report. However, the

aspects related to berms, slopes and roughness elements are dealt with when they have

an influence on wave run-up and wave overtopping.

2.3 Wave conditions

In defining the wave climate at the site, the ideal situation is to collect long term

instrumentally measured data at the required location. There are very few instances in

which this is even a remote possibility. The data of almost 30 years’ of wave height

measurements is shown in Figure 2.3. These are the Dutch part of the North Sea with an

extrapolation to very extreme events.

It is however more likely that data in deep water, offshore of a site will be available either

through the use of a computational wave prediction model based on wind data, or on a

wave model. In both of these cases the offshore data can be used in conjunction with a

wave transformation model to provide information on wave climate at a coastal site. If

instrumentally measured data is also available, covering a short period of time, this can be

used for the calibration or verification of the wave transformation model, thus giving

greater confidence in its use.

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Figure 2.3: Wave measurements and numerical simulations in the North Sea (1964-1993),

leading to an extreme distribution

Wind generated waves offshore of most coasts have wave periods in the range 1s to 20s.

The height, period and direction of the waves generated will depend on the wind speed,

duration, direction and the 'fetch', i.e. the unobstructed distance of sea surface over which

the wind has acted. In most situations, one of either the duration or fetch become

relatively unimportant. For example, in an inland reservoir or lake, even a short storm will

produce large wave heights. However, any increase in the duration of the wind will then

cause no extra growth because of the small fetch lengths. Thus such waves are

described as 'fetch limited". In contrast, on an open coast where the fetch is very large

but the wind blows for only a short period, the waves are limited by the duration of the

storm. Beyond a certain limit, the exact fetch length becomes unimportant. These waves

are described as ‘duration limited'.

On oceanic shorelines the situation is usually more complicated. Both the fetch and

duration may be extremely large, waves then become "fully developed" and their height

depends solely on the wind speed. In such situations the wave period usually becomes

quite large, and long period waves are able to travel great distances without suffering

serious diminution. The arrival of ‘swell’, defined as waves not generated by local and/or

recent wind conditions, presents a more challenging situation from the viewpoint of wave

predictions.

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2.4 Wave conditions at depth-limited situations

Wave breaking remains one phenomenon that is difficult to describe mathematically. One

reason for this is that the physics of the process is not yet completely understood.

However, as breaking has a significant effect on the behaviour of waves, the transport of

sediments, the magnitude of forces on coastal structures and the overtopping response, it

is represented in computational models. The most frequent method for doing this is to

define an energy dissipation term which is used in the model when waves reach a limiting

depth compared to their height.

There are also two relatively simple empirical methods for a first estimate of the incident

wave conditions in the surf zone. The methods by Goda (1980) and Owen (1980) are

regularly used. Goda (1980) inshore wave conditions are influenced by shoaling and

wave breaking. These processes are influenced by a number of parameters such as the

sea steepness and the slope of the bathymetry. To take all the important parameters into

account Goda (1980) provided a series of graphs to determine the largest and the

significant wave heights (Hmax and Hs) for 1:10, 1:20, 1:30 and 1:100 sloping bathymetries.

Results obtained from a simple 1D energy decay numerical model (Van der Meer, 1990)

in which the influence of wave breaking is included, are presented in Figure 2.4. This

method has also been described in the Rock Manual (1991) and the updated version of

this Rock Manual (2007). Tests have shown that wave height predictions using the

design graphs from this model are accurate for slopes ranging from 1:10 to 1:100. For

slopes flatter than 1:100, the predictions for the 1:100 slopes should be used.

The method for using these graphs is:

1. Determine the deep-water wave steepness, sop = Hso/Lop (where Lop = gTp2/(2π)).

This value determines which graphs should be used. Suppose here for

convenience that sop = 0.043, then the graphs of Figure 2.4 for sop = 0.04 and 0.05

have to be used, interpolating between the results from each.

2. Determine the local relative water depth, h/Lop. The range of the curves in the

graphs covers a decrease in wave height by 10 per cent to about 70 per cent.

Limited breaking occurs at the right hand side of the graphs and severe breaking

on the left-hand side. If h/Lop is larger than the maximum value in the graph this

means that there is no or only limited wave breaking and one can then assume no

wave breaking (deep-water wave height = shallow-water wave height).

3. Determine the slope of the foreshore (m = tan α). Curves are given for range

m = 0.075 to 0.01 (1:13 to 1:100). For gentler slopes the 1:100 slope should be

used.

4. Enter the two selected graphs with calculated h/Lop and read the breaker index

Hm0/h from the curve of the calculated foreshore slope.

5. Interpolate linearly between the two values of Hm0/h to find Hm0/h for the correct

wave steepness.

Example. Suppose Hso = 6 m, Tp = 9.4 s, foreshore slope is 1:40 (m = 0.025). Calculate

the maximum significant wave height Hm0 at a water depth of h = 7 m.

1. The wave conditions on deep water give sop = 0.043. Graphs with sop = 0.04 and

0.05 have to be used.

2. The local relative water depth h/Lop = 0.051.

3. The slope of the foreshore (m = 0.025) is in between the curves for m = 0.02 and

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4. From the graphs, Hm0/h = 0.64 is found for sop = 0.04 and 0.68 is found for

sop = 0.05.

5. Interpolation for sop = 0.043 gives Hm0/h = 0.65 and finally a depth-limited spectral

significant wave height of Hm0 = 3.9 m.

Figure 2.4: Depth-limited significant wave heights for uniform foreshore slopes

Wave breaking in shallow water does not only affect the significant wave height Hm0. Also

the distribution of wave heights will change. In deep water wave heights have a Rayleigh

distribution and the spectral wave height Hm0 will be close to the statistical wave height

H1/3. In shallow water these wave heights become different values due to the breaking

process. Moreover, the highest waves break first when they feel the bottom, where the

small waves stay unchanged. Actually, this gives a non-homogeneous set of wave

heights: broken waves and non-broken waves. For this reason Battjes and Groenendijk

(2000) developed the composite Weibull distribution for wave heights in shallow water.

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Although prediction methods in this manual are mainly based on the spectral significant

wave height, it might be useful in some cases to consider also other definitions, like the

2%-wave height H2% or H1/10, the average of the highest 1/10-the of the waves. For this

reason a summary of the method of Battjes and Groenendijk (2000) is given here. The

example given above with a calculated Hm0 = 3.9 m at a depth of 7m on a 1:40 slope

foreshore has been explored further in Figure 2.5.

00 4 mHm = Hm0 = 4 0m

( ) 0024.369.2 mhmHrms +=

where Hrms = root mean square wave height. The transition wave height, Htr, between the

lower Rayleigh distribution and the higher Weibull distribution (see Figure 2.5) is then

given by:

( )hHtr αtan8.535.0 += 2.2

One has then to compute the non-dimensional wave height Htr/Hrms, which is used as input

to Table 2 of Battjes and Groenendijk (2000) to find the (non-dimensional) characteristic

heights: H1/3/Hrms, H1/10/Hrms, H2%/Hrms, H1%/Hrms and H0.1%/Hrms. Some particular values

have been extracted from this table and are included in Table 2.1, only for the ratios

H1/3/Hrms, H1/10/Hrms, and H2%/Hrms.

probability of exceedance (%)

w av e he ig ht (m

Rayleigh distribution

Weibull

distribution

Transition wave height Htr

w av e he ig ht (m

Figure 2.5: Computed composite Weibull distribution. Hm0 = 3.9 m; foreshore slope 1:40 and

water depth h = 7 m

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Table 2.1: Values of dimensionless wave heights for some values of Htr/Hrms

Non-dimensional transitional wave Htr/Hrms Characteristic

height 0.05 0.50 1.00 1.20 1.35 1.50 1.75 2.00 2.50 3.00

The final step is the computation of the dimensional wave heights from the ratios read in

the table and the value of Hrms. For the given example one finds: H1/3 = 4.16 m;

H1/10 = 4.77 m and H2% = 5.4 m. Note that the value H2%/H1/3 changed from 1.4 for a

Rayleigh distribution (see Figure 2.5) to a value of 1.21.

2.5 Currents

Where waves are propagating towards an oncoming current, for example at the mouth of

a river, the current will tend to increase the steepness of the waves by increasing their

height and decreasing their wave length. Refraction of the waves by the current will tend

to focus the energy of the waves towards the river mouth. In reality both current and

depth refraction are likely to take place producing a complex wave current field. It is

clearly more complicated to include current and depth refraction effects, but at sites where

currents are large they will have a significant influence on wave propagation.

Computational models are available to allow both these effects to be represented.

2.6 Application of design conditions

The selection of a given return period for a particular site will depend on several factors.

These will include the expected lifetime of the structure, expected maximum wave and

water level conditions and the intended use of the structure. If for instance the public are

to have access to the site then a higher standard of defence will be required than that to

protect farm land. Further examples are given in Chapter 3.

A way of considering an event with a given return period, TR, is to consider that (for TR ≥ 5

years) the probability of its occurrence in any one year is approximately equal to 1/TR. For

example, a 10,000 year return period event is equivalent to one with a probability of

occurrence of 10-4 in any one year.

Over an envisaged lifetime of N years for a structure (not necessarily the same as the

design return period) the probability of encountering the wave condition with return period

TR, at least once, is given by:

Figure 2.6 presents curves for this encounter probability with values between 1 per cent

and 80 per cent shown as a function of TR and N. It follows that there will not be exactly

TR years between events with a given return period of TR years. It can be seen that for a

time interval equal to the return period, there is a 63% chance of occurrence within the

return period. Further information on design events and return periods can be found in

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the British Standard Code of practice for Maritime Structures BS6349 Part 1 1974 and

Part 7 1991), the PIANC working group 12 report (PIANC 1992) and in the new Rock

Manual (2007).

Figure 2.6: Encounter probability

2.7 Uncertainties in inputs

Principal input parameters discussed in this section comprised water levels, including

tides, surges, and sea level changes. Sea state parameters at the toe of the structure

have been discussed and river discharges and currents have been considered.

It is assumed here that all input parameters are made available at the toe of the structure.

Depending on different foreshore conditions and physical processes such as refraction,

shoaling and wave breaking the statistical distributions of those parameters will have

changed over the foreshore. Methods to account for this change are given in Battjes &

Groenendijk (2000) and elsewhere.

If no information on statistical distributions or error levels is available for water levels or

sea state parameters the following assumptions should be taken: all parameters are

normally distributed; significant wave height Hs or mean wave height Hm0 have a

coefficient of variation σx’ = 5.0%; peak wave period Tp or mean wave period Tm-1.0 have a

coefficient of variation σx’ = 5.0%;and design water level at the toe σx’ = 3.0%, see

Schüttrumpf et al. (2006).

The aforementioned values were derived from expert opinions on these uncertainties.

About 100 international experts and professionals working in coastal engineering have

been interviewed for this purpose. Although these parameters may be regarded rather

small in relation to what Goda (1985) has suggested results have been tested against real

cases and found to give a reasonable range of variations. It should be noted that these

uncertainties are applied to significant values rather than mean sea state parameters.

This will both change the type of the statistical distribution and the magnitude of the

standard deviation or the coefficient of variation.

Guidance on hydraulic boundary conditions for the safety assessment of Dutch water

defences can be found in Hydraulische Randvoorwaarden, RWS 2001 (Due to be updated

in 2007).

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3.1 Introduction

Most sea defence structures are constructed primarily to limit overtopping volumes that

might cause flooding. Over a storm or tide, the overtopping volumes that can be tolerated

will be site specific as the volume of water that can be permitted will depend on the size

and use of the receiving area, extent and magnitude of drainage ditches, damage versus

inundation curves, and return period. Guidance on modelling inundation flows is being

developed within Floodsite (FLOODSITE), but flooding volumes and flows, per se, are not

distinguished further in this chapter.

For sea defences that protect people living, working or enjoying themselves, designers

and owners of these defences must, however, also deal with potential direct hazards from

overtopping. This requires that the level of hazard and its probability of occurrence be

assessed, allowing appropriate action plans to be devised to ameliorate risks arising from

overtopping.

The main hazards on or close to sea defence structures are of death, injury, property

damage or disruption from direct wave impact or by drowning. On average, approximately

2-5 people are killed each year in each of UK and Italy through wave action, chiefly on

seawalls and similar structures (although this rose to 11 in UK during 2005). It is often

helpful to analyse direct wave and overtopping effects, and their consequences under four

general categories:

a) Direct hazard of injury or death to people immediately behind the defence;

b) Damage to property, operation and / or infrastructure in the area defended,

including loss of economic, environmental or other resource, or disruption to an

economic activity or process;

c) Damage to defence structure(s), either short-term or longer-term, with the

possibility of breaching and flooding.

d) Low depth flooding (inconvenient but not dangerous)

The character of overtopping flows or jets, and the hazards they cause, also depend upon

the geometry of the structure and of the immediate hinterland behind the seawall crest,

and the form of overtopping. For instance, rising ground behind the seawall may permit

visibility of incoming waves, and will slow overtopping flows. Conversely, a defence that is

elevated significantly above the land defended may obscure visibility of incoming waves,

and post-overtopping flows may increase in speed rather than reduce. Hazards caused

by overtopping therefore depend upon both the local topography and structures as well as

on the direct overtopping characteristics.

It is not possible to give unambiguous or precise limits to tolerable overtopping for all

conditions. Some guidance is, however, offered here on tolerable mean discharges and

maximum overtopping volumes for a range of circumstances or uses, and on inundation

flows and depths. These limits may be adopted or modified depending on the

circumstances and uses of the site.

3.1.1 Wave overtopping processes and hazards

Hazards driven by overtopping can be linked to a number of simple direct flow

parameters:

• mean overtopping discharge, q;

• individual and maximum overtopping volumes, Vi and Vmax;

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• overtopping velocities over the crest or promenade, horizontally and vertically, vxc

and vzc or vxp and vzp;

• overtopping flow depth, again measured on crest or promenade, dxc or dxp.

Less direct responses (or similar responses, but farther back from the defence) may be

used to assess the effects of overtopping, perhaps categorised by:

• overtopping falling distances, xc;

• post-overtopping wave pressures (pulsating or impulsive), pqs or pimp;

• post-overtopping flow depths, dxc or dxp; and horizontal velocities, vxc or vxp.

The main response to these hazards has most commonly been the construction of new

defences, but responses should now always consider three options, in increasing order of

intervention:

a) Move human activities away from the area subject to overtopping and/or flooding

hazard, thus modifying the land use category and/or habitat status;

b) Accept hazard at a given probability (acceptable risk) by providing for temporary

use and/or short-term evacuation with reliable forecast, warning and evacuation

systems, and/or use of temporary / demountable defence systems;

c) Increase defence standard to reduce risk to (permanently) acceptable levels

probably by enhancing the defence and / or reducing loadings.

For any structure expected to ameliorate wave overtopping, the crest level and/or the front

face configuration will be dimensioned to give acceptable levels of wave overtopping

under specified extreme conditions or combined conditions (e.g. water level and waves).

Setting acceptable levels of overtopping depends on:

• the use of the defence structure itself;

• use of the land behind;

• national and/or local standards and administrative practice;

• economic and social basis for funding the defence.

Under most forms of wave attack, waves tend to break before or onto sloping

embankments with the overtopping process being relatively gentle. Relatively few water

levels and wave conditions may cause “impulsive” breaking where the overtopping flows

are sudden and violent. Conversely, steeper, vertical or compound structures are more

likely to experience intense local impulsive breaking, and may overtop violently and with

greater velocities. The form of breaking will therefore influence the distribution of

overtopping volumes and their velocities, both of which will impact on the hazards that

they cause.

Additional hazards that are not dealt with here are those that arise from wave reflections,

often associated with steep faced defences. Reflected waves increase wave disturbance,

which may cause hazards to navigating or moored vessels; may increase waves along

neighbouring frontages, and/or may initiate or accelerate local bed erosion thus increasing

depth-limited wave heights (see section 2.4).

3.1.2 Types of overtopping

Wave overtopping which runs up the face of the seawall and over the crest in (relatively)

complete sheets of water is often termed ‘green water’. In contrast, ‘white water’ or spray

overtopping tends to occur when waves break seaward of the defence structure or break

onto its seaward face, producing non-continuous overtopping, and/or significant volumes

of spray. Overtopping spray may be carried over the wall either under its own momentum,

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or assisted and/or driven by an onshore wind. Additional spray may also be generated by

wind acting directly on wave crests, particularly when reflected waves interact with

incoming waves to give severe local ‘clapotii’. This type of spray is not classed as

overtopping nor is it predicted by the methods described in this manual.

Without a strong onshore wind, spray will seldom contribute significantly to overtopping

volumes, but may cause local hazards. Light spray may reduce visibility for driving,

important on coastal highways, and will extend the spatial extent of salt spray effects such

as damage to crops / vegetation, or deterioration of buildings. The effect of spray in

reducing visibility on coastal highways (particularly when intermittent) can cause sudden

loss of visibility in turn leading drivers to veer suddenly.

Effects of wind and generation of spray have not often been modelled. Some research

studies have suggested that effects of onshore winds on large green water overtopping

are small, but that overtopping under q = 1 l/s/m might increase by up to 4 times under

strong winds, especially where much of the overtopping is as spray. Discharges between

q = 1 to 0.1 l/s/m are however already greater than some discharge limits suggested for

pedestrians or vehicles, suggesting that wind effects may influence overtopping at and

near acceptable limits for these hazards.

Figure 3.1: Overtopping on embankment and promenade seawalls

3.1.3 Return periods

Return periods at which overtopping hazards are analysed, and against which a defence

might be designed, may be set by national regulation or guidelines. As with any area of

risk management, different levels of hazard are likely to be tolerated at inverse levels of

probability or return period. The risk levels (probability x consequence) that can be

tolerated will depend on local circumstances, local and national guidelines, the balance

between risk and benefits, and the level of overall exposure. Heavily trafficked areas

might therefore be designed to experience lower levels of hazard applied to more people

than lightly used areas, or perhaps the same hazard level at longer return periods.

Guidance on example return periods used in evaluating levels of protection suggest

example protection levels versus return periods as shown in Table 3.1.

In practice, some of these return periods may be regarded as too short. National

guidelines have recommended lower risk, e.g. a low probability of flooding in UK is now

taken as <0.1% probability (1:1000 year return) and medium probability of sea flooding as

between 0.5% and 0.1% (1:200 to 1:1000 year return). Many existing sea defences in the

UK however offer levels of protection far lower than these.

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Table 3.1: Hazard Type

Design life Level of Protection(1) Hazard type and reason

(years) (years)

Temporary or short term measures 1-20 5-50

Majority of coast protection or sea defence walls 30-70 50-100

Flood defences protecting large areas at risk 50-100 100-10,000

Special structure, high capital cost 200 Up to 10,000

Nuclear power stations etc - 10,000

(1) Note: Total probability return period

It is well known that the Netherlands is low-lying with two-thirds of the country below storm

surge level. Levels of protection were increased after the flood in 1953 where almost

2000 people drowned. Large rural areas have a level of protection of 10,000 years, less

densely populated areas a level of 4,000 years and protection for high river discharge

(without threat of storm surge) of 1,250 years.

The design life for flood defences, like dikes, which are fairly easy to upgrade, is taken in

the Netherlands as 50 years. In urban areas, where it is more difficult to upgrade a flood

defence, the design life is taken as 100 years. This design life increases for very special

structures with high capital costs, like the Eastern Scheldt storm surge barrier, Thames

barrier, or the Maeslandtkering in the entrance to Rotterdam. A design life of around 200

years is then usual.

Variations from simple “acceptable risk” approach may be required for publicly funded

defences based on benefit – cost assessments, or where public aversion to hazards

causing death require greater efforts to ameliorate the risk, either by reducing the

probability of the hazard or by reducing its consequence.

3.2 Tolerable mean discharges

Guidance on overtopping discharges that can cause damage to seawalls, buildings or

infrastructure, or danger to pedestrians and vehicles have been related to mean

overtopping discharges or (less often) to peak volumes. Guidance quoted previously

were derived initially from analysis in Japan of overtopping perceived by port engineers to

be safe (Goda et al. (1975), Fukuda et al. (1974)). Further guidance from Iceland

suggests that equipment or cargo might be damaged for q ≥ 0.4 l/s/m. Significantly

different limits are discussed for embankment seawalls with back slopes; or for

promenade seawalls without back slopes. Some guidance distinguishes between

pedestrians or vehicles, and between slow and faster speeds for vehicles.

Tests on the effects of overtopping on people suggest that information on mean

discharges alone may not give reliable indicators of safety for some circumstances, and

that maximum individual volumes may be better indicators of hazard than average

discharges. The volume (and velocity) of the largest overtopping event can vary

significantly with wave condition and structure type, even for a given mean discharge.

There remain however two difficulties in specifying safety levels with reference to

maximum volumes rather than to mean discharges. Methods to predict maximum

volumes are available for fewer structure types, and are less well-validated. Secondly,

data relating individual maximum overtopping volumes to hazard levels are still very rare.

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In most instances the discharge (or volumes) discussed here are those at the point of

interest, e.g. at the roadway or footpath or building. It is noted that the hazardous effect of

overtopping waters reduces with the distance away from the defence line. As a rule of

thumb, the hazard effect of an overtopping discharge at a point x metres back from the

seawall crest will be to reduce the overtopping discharge by a factor of x, so the effective

overtopping discharge at x (over a range of 5 - 25m), qeffective is given by:

xqq seawalleffective = 3.1

The overtopping limits suggested in Table 3.2 to Table 3.5 therefore derive from a

generally precautionary principle informed by previous guidance and by observations and

measurements made by the CLASH partners and other researchers. Limits for

pedestrians in Table 3.2 show a logical sequence, with allowable discharges reducing

steadily as the recipient’s ability or willingness to anticipate or receive the hazard reduces.

Table 3.2: Limits for overtopping for pedestrians

Mean discharge Max volume(1) Hazard type and reason

q (l/s/m) Vmax (l/m)

Trained staff, well shod and protected, expecting to

get wet, overtopping flows at lower levels only, no

falling jet, low danger of fall from walkway

1 – 10 500 at low level

Aware pedestrian, clear view of the sea, not easily

upset or frightened, able to tolerate getting wet, wider

walkway(2).

at high level

or velocity

(1) Note: These limits relate to overtopping velocities well below vc ≈ 10 m/s. Lower volumes may be

required if the overtopping process is violent and/or overtopping velocities are higher.

(2) Note: Not all of these conditions are required, nor should failure of one condition on its own

require the use of a more severe limit

A further precautionary limit of q = 0.03 l/s/m might apply for unusual conditions where

pedestrians have no clear view of incoming waves; may be easily upset or frightened or

are not dressed to get wet; may be on a narrow walkway or in close proximity to a trip or

fall hazard. Research studies have however shown that this limit is only applicable for the

conditions identified, and should NOT be used as the general limit for which q = 0.1 l/s/m

in Table 3.2 is appropriate.

For vehicles, the suggested limits are rather more widely spaced as two very different

situations are considered. The higher overtopping limit in Table 3.3 applies where wave

overtopping generates pulsating flows at roadway level, akin to driving through

slowly-varying fluvial flow across the road. The lower overtopping limit in Table 3.3 is

however derived from considering more impulsive flows, overtopping at some height

above the roadway, with overtopping volumes being projected at speed and with some

suddenness. These lower limits are however based on few site data or tests, and may

therefore be relatively pessimistic.

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Table 3.3: Limits for overtopping for vehicles

Mean

discharge

Max

volume Hazard type and reason

q (l/s/m) Vmax (l/m)

Driving at low speed, overtopping by pulsating flows at

low flow depths, no falling jets, vehicle not immersed 10 – 50

Driving at moderate or high speed, impulsive

overtopping giving falling or high velocity jets 0.01 – 0.05

at high level

or velocity

(1) Note: These limits probably relate to overtopping defined at highway.

(2) Note: These limits relate to overtopping defined at the defence, but assumes the highway to be

immediately behind the defence.

Rather fewer data are available on the effects of overtopping on structures, buildings and

property. Site-specific studies suggest that pressures on buildings by overtopping flows

will vary significantly with the form of wave overtopping, and with the use of sea defence

elements intended to disrupt overtopping momentum (not necessarily reducing

discharges). Guidance derived from the CLASH research project and previous work

suggests limits in Table 3.4 for damage to buildings, equipment or vessels behind

defences.

Table 3.4: Limits for overtopping for property behind the defence

Mean

discharge

Max

volume Hazard type and reason

q (l/s/m) Vmax (l/m)

Significant damage or sinking of larger yachts 50 5,000 – 50,000

Sinking small boats set 5-10m from wall.

Damage to larger yachts 10

Building structure elements 1(2) ~

Damage to equipment set back 5-10m 0.4(1) ~

(1) Note: These limits relate to overtopping defined at the defence.

(2) Note: This limit relates to the effective overtopping defined at the building.

A set of limits for defence structures in Table 3.5 have been derived from early work by

Goda and others in Japan. These give a first indication of the need for specific protection

to resist heavy overtopping flows. It is assumed that any structure close to the sea will

already be detailed to resist the erosive power of heavy rainfall and/or spray. Two

situations are considered, see Figure 3.1: Embankment seawalls or sea dikes with the

defence structure elevated above the defended area, so overtopping flows can pass over

the crest and down the rear face; or promenade defences in which overtopping flows

remain on or behind the seawall crest before returning seaward. The limits for the latter

category cannot be applied where the overtopping flows can fall from the defence crest

where the nature of the flow may be more impulsive.

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Table 3.5: Limits for overtopping for damage to the defence crest or rear slope

Mean

discharge Hazard type and reason

q (l/s/m)

Embankment seawalls / sea dikes

No damage if crest and rear slope are well protected 50-200

No damage to crest and rear face of grass covered

embankment of clay 1-10

No damage to crest and rear face of embankment if

not protected 0.1

Promenade or revetment seawalls

Damage to paved or armoured promenade behind

seawall 200

Damage to grassed or lightly protected promenade or

reclamation cover 50

Wave overtopping tests were performed in early 2007 on a real dike in the Netherlands.

The dike had a 1:3 inner slope of fairly good clay (sand content smaller than 30%) with a

grass cover. The wave overtopping simulator (see Section 3.3.3) was used to test the

erosion resistance of this inner slope. Tests were performed simulating a 6 hour storm for

every overtopping condition at a constant mean overtopping discharge. These conditions

started with a mean discharge of 0.1 l/s/m and increased to 1; 10; 20; 30 and finally even

50 l/s/m. After all these simulated storms the slope was still in good condition and showed

little erosion. The erosion resistance of this dike was very high.

Another test was performed on bare clay by removing the grass sod over the full inner

slope to a depth of 0.2 m. Overtopping conditions of 0.1 l/s/m; 1; 5 and finally 10 l/s/m

were performed, again for 6 hours each. Erosion damage started for the first condition

(two erosion holes) and increased during the other overtopping conditions. After 6 hours

at a mean discharge of 10 l/s/m (see Figure 3.2) there were two large erosion holes, about

1 m deep, 1 m wide and 4 m long. This situation was considered as “not too far from

initial breaching”.

The overall conclusion of this first overtopping test on a real dike is that clay with grass

can be highly erosion resistant. Even without grass the good quality clay also survived

extensive overtopping. The conclusions may not yet be generalized to all dikes as clay

quality and type of grass cover still may play a role and, therefore, more testing is required

to come to general conclusions.

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Figure 3.2: Wave overtopping test on bare clay; result after 6 hours with 10 l/s per m width

One remark, however, should be made on the strength of the inner slopes of dikes by

wave overtopping. Erosion of the slope is one of the possible failure mechanisms. The

other one, which happened often in the past, is a slip failure of the slope. Slip failures

may directly lead to a breach, but such slip failures occur mainly for steep inner slopes like

1:1.5 or 1:2. For this reason most dike designs in the Netherlands in the past fifty years

have been based on a 1:3 inner slope, where it is unlikely that slip failures will occur due

to overtopping. This mechanism might however occur for steep inner slopes, so should

be taken into account in safety analysis.

3.3 Tolerable maximum volumes and velocities

3.3.1 Overtopping volumes

Guidance on suggested limits for maximum individual overtopping volumes have been

given in Table 3.2 to Table 3.5 where data are available. Research studies with

volunteers at full scale or field observations suggest that danger to people or vehicles

might be related to peak overtopping volumes, with “safe” limits for people covering:

Vmax = 1000 to 2000 l/m for trained and safety-equipped staff in pulsating flows on

a wide-crested dike;

Vmax = 750 l/m for untrained people in pulsating flows along a promenade;

Vmax = 100 l/m for overtopping at a vertical wall

Vmax = 50 l/m where overtopping could unbalance an individual by striking their

upper body without warning.

3.3.2 Overtopping velocities

Few data are available on overtopping velocities and their contribution to hazards. For

simply sloping embankments Chapter 5 gives guidance on overtopping flow velocities at

crest and inner slope as well as on flow depths. Velocities of 5-8 m/s are possible for the

maximum overtopping waves during overtopping discharges of about 10-30 l/s per m

width. Studies of hazards under steady flows suggest that limits on horizontal velocities

for people and vehicles will probably need to be set below vx < 2.5 to 5m/s. Also refer to

Section 5.5.

Upward velocities (vz) for vertical and battered walls under impulsive and pulsating

conditions have been related to the inshore wave celerity, see Chapter 7. Relative

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velocities, vz/ci, have been found to be roughly constant at vz/ci ≈ 2.5 for pulsating and

slightly impulsive conditions, but increase significantly for impulsive conditions, reaching

vz/ci ≈ 3 – 7.

3.3.3 Overtopping loads and overtopping simulator

Post-overtopping wave loads have seldom been measured on defence structures,

buildings behind sea defences, or on people, so little generic guidance is available. If

loadings from overtopping flows could be important, they should be quantified by

interpretation of appropriate field data or by site-specific model studies.

An example (site specific) model study indicates how important these effects might be. A

simple 1m high vertical secondary wall was set in a horizontal promenade about 7m back

from the primary seawall, itself a concrete recurve fronted by a rock armoured slope.

Pulsating wave pressures were measured on the secondary wall against the effective

overtopping discharge arriving at the secondary wall, plotted here in Figure 3.3. This was

deduced by applying Equation 3.1 to overtopping measured at the primary wall, 7m in

front. Whilst strongly site specific, these results suggest that quite low discharges

(0.1-1.0 l/s/m) may lead to loadings up to 5kPa.

Overtopping discharge at the seawall [l/s/m]

Pr es su re [k Pa

Pqs

Linear (Pqs)

Figure 3.3: Example wave forces on a secondary wall

During 2007, a new wave overtopping simulator was developed to test the erosion

resistance of crest and inner slope of a dike, starting from the idea that:

• knowledge on wave breaking on slopes and overtopping discharges is sufficient

(Chapter 5);

• knowledge on the pattern of overtopping volumes, distributions, velocities and flow

depth of overtopping water on the crest, is sufficient as well (Chapter 5);

• only the overtopping part of the waves need to be simulated;

• tests can be performed in-situ on each specific dike, which is much cheaper than

testing in a large wave flume.

The simulator was developed and designed within the ComCoast, see Figure 3.4. Results

of the calibration phase with a 1m wide prototype were described by Van der Meer (2006).

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Figure 3.4: Principle of the wave overtopping simulator

Figure 3.5: The wave overtopping simulator discharging a large overtopping volume on the inner

slope of a dike

The simulator consists of a mobile box (adjustable in height) to store water. The

maximum capacity is 3.5 m3 per m width (14 m3 for the final, 4 m wide, simulator see

Figure 3.5). This box is filled continuously with a predefined discharge q and emptied at

specific times through a butterfly valve in such a way that it simulates the overtopping

tongue of a wave at the crest and inner slope of a dike. As soon as the box contains the

required volume, V, the valve is opened and the water is released on a transition section

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that leads to the crest of the dike. The discharge is released such that flow velocity,

turbulence and thickness of the water tongue at the crest corresponds with the

characteristics that can be expected (see Chapter 5). The calibration (Van der Meer,

2006) showed that it is possible to simulate the required velocities and flow depths for a

wide range of overtopping rates, significantly exceeding present standards.

3.4 Effects of debris and sediment in overtopping flows

There are virtually no data on the effect of debris on hazards caused by overtopping,

although anecdotal comments suggest that damage can be substantially increased for a

given overtopping discharge or volume if “hard” objects such as rocks, shingle or timber

are included in overtopping. It is known that impact damage can be particularly noticeable

for seawalls and promenades where shingle may form the “debris” in heavy or frequent

overtopping flows.

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4.1 Introduction

A number of different methods may be available to predict overtopping of particular

structures (usually simplified sections) under given wave conditions and water levels.

Each method will have strengths or weaknesses in different circumstances. In theory, an

analytical method can be used to relate the driving process (waves) and the structure to

the response through equations based directly on a knowledge of the physics of the

process. It is however extremely rare for the structure, the waves and the overtopping

process to all be so simple and well-controlled that an analytical method on its own can

give reliable predictions. Analytical methods are not therefore discussed further in this

manual.

The primary prediction methods are therefore based on empirical methods (Section 4.2)

that relate the overtopping response (usually mean overtopping discharge) to the main

wave and structure parameters. Two other methods have been derived during the

CLASH European project based on the use of measured overtopping from model tests

and field measurements. The first of these techniques uses the CLASH database of

structures, waves and overtopping discharges, with each test described by 13

parameters. Using the database (Section 4.5) is however potentially complicated,

requiring some familiarity with these type of data. A simpler approach, and much more

rapid, is to use the Neural Network tool (Section 4.3) that has been trained using the test

results in the database. The Neural Network tool can be run automatically on a computer

as a stand-alone device, or embedded within other simulation methods.

For situations for which empirical test data do not already exist, or where the methods

above do not give reliable enough results, then two alternative methods may be used, but

both are more complicated than the three methods described in Sections 4.2 to 4.5. A

range of numerical models can be used to simulate the process of overtopping

(Section 4.6). All such models involve some simplification of the overtopping process and

are therefore limited to particular types of structure or types of wave exposure. They may

however run sequences of waves giving overtopping (or not) on a wave-by-wave basis.

Generally, numerical models require more skill and familiarity to run successfully.

The final method discussed here is physical modelling in which a scale model is tested

with correctly scaled wave conditions. Typically such models may be built to a geometric

scale typically in the range 1:20 to 1:60, see discussion on model and scale effects in

Section 4.8. Waves will be generated as random wave trains each conforming to a

particular energy spectrum. The model may represent a structure cross-section in a

2-dimensional model tested in a wave flume. Structures with more complex plan shapes,

junctions, transitions etc., may be tested in a 3-dimensional model in a wave basin.

Physical models can be used to measure many different aspects of overtopping such as

wave-by-wave volumes, overtopping velocities and depths, as well as other responses.

4.2 Empirical models, including comparison of structures

4.2.1 Mean overtopping discharge

Empirical methods use a simplified representation of the physics of the process presented

in (usually dimensionless) equations to relate the main response parameters (overtopping

discharge etc) to key wave and structure parameters. The form and coefficients of the

equations are adjusted to reproduce results from physical model (or field) measurements

of waves and overtopping.

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Empirical equations may be solved explicitly, or may occasionally require iterative

methods to solve. Historically some empirical methods have been presented graphically,

although this is now very rare.

The mean overtopping discharge, q, is the main parameter in the overtopping process. It

is of course not the only parameter, but it is easy to measure in a laboratory wave flume or

basin, and most other parameters are related in some way to this overtopping discharge.

The overtopping discharge is given in m3/s per m width and in practical applications often

in litres/s per m width. Although it is given as a discharge, the actual process of wave

overtopping is much more dynamic. Only large waves will reach the crest of the structure

and will overtop with a lot of water in a few seconds. This wave by wave overtopping is

more difficult to measure in a laboratory than the mean overtopping discharge.

As the mean overtopping discharge is quite easy to measure many physical model tests

have been performed all over the world, both for scientific (idealised) structures and real

applications or designs. The European CLASH project resulted in a large database of

more than 10,000 wave overtopping tests on all kind of structures (see Section 4.5).

Some series of tests have been used to develop empirical methods for prediction of

overtopping. Very often the empirical methods or formulae are applicable for typical

structures only, like smooth slopes (dikes, sloping seawalls), rubble mound structures or

vertical structures (caissons) or walls.

Chapters 5, 6 and 7 will describe in detail formulae for the different kinds of structure. In

this section an overall view will be given in order to compare different structures and to

give more insight into how wave overtopping behaves for different kind of structures. The

structures considered here with governing overtopping equations (more details in

Chapters 5, 6 and 7) are: smooth sloping structures (dikes, seawalls); rubble mound

structures (breakwaters, rock slopes); and vertical structures (caissons, sheet pile walls).

The principal formula used for wave overtopping is:

)/exp( 03

mc m HbRa

gH q −= 4.1

It is an exponential function with the dimensionless overtopping discharge q/(gHm03)½ and

the relative crest freeboard Rc/Hm0. This type of equation shown in a log-linear graph

gives a straight line, which makes it easy to compare the formulae for various structures.

Specific equations are given in Chapters 5 and 6 for smooth and rubble mound structures

and sometimes include a berm, oblique wave attack, wave walls and the slope angle and

wave period or wave steepness.

Two equations are considered for pulsating waves on a vertical structure. Allsop

et al. (1995) consider relatively shallow water and Franco et al. (1994) more deep water

(caissons). Vertical structures in shallow water, and often with a sloping foreshore in

front, may become subject to impulsive forces, i.e. high impacts and water splashing high

up into the air. Specific formulae have been developed for these kinds of situation.

For easy comparison of different structures, like smooth and rubble mound sloping

structures and vertical structures for pulsating and impulsive waves, some simplifications

will be assumed.

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In order to simplify the smooth structure no berm is considered (γb = 1), only perpendicular

wave attack is present (γβ = 1), and no vertical wall on top of the structure is present

(γv = 1). As a smooth structure is considered also, γf = 1. This limits the structure to a

smooth and straight slope with perpendicular wave attack. The slope angles considered

for smooth slopes are cotα = 1 to 8, which means from very steep to very gentle. If

relevant a wave steepness of so = 0.04 (steep storm waves) and 0.01 (long waves due to

swell or wave breaking) will be considered.

The same equation as for smooth sloping structures is applicable for rubble mound

slopes, but now with a roughness factor of γf = 0.5, simulating a rock structure. Rubble

mound structures are often steep, but rock slopes may also be gentle. Therefore slope

angles with cotα = 1.5 and 4.0 are considered.

For vertical structures under pulsating waves both formulae of Allsop et al. (1995) and

Franco et al. (1994) will be compared, together with the formula for impulsive waves.

Impulsive waves can only be reached with a relatively steep foreshore in front of the

vertical wall. For comparison values of the ratio wave height/water depth of Hm0/hs = 0.5,

0.7 & 0.9 will be used.

Smooth slopes can be compared with rubble mound slopes and with vertical structures

under pulsating or impulsive conditions. First the traditional graph is given in Figure 4.1

with the relative freeboard Rc/Hm0 versus the logarithmic dimensionless overtopping

q/(gHm03)½.

In most cases the steep smooth slope gives the largest overtopping. Steep means

cotα < 2, but also a little gentler if long waves (small steepness) are considered. Under

these conditions waves surge up the steep slope. For gentler slopes waves break as

plunging waves and this reduces wave overtopping. The gentle slope with cotα = 4 gives

much lower overtopping than the steep smooth slopes. Both slope angle and wave period

have influence on overtopping for gentle slopes.

The large roughness and high permeability of a rubble mound structures reduces wave

overtopping to a greater extent; see Figure 4.1. A roughness factor of γf = 0.5 was used

and a value of 0.4 (two layers of rock on a permeable under layer) would even reduce the

overtopping further. The gentle rubble mound slope with cotα = 4 gives very low

overtopping.

Vertical structures under pulsating waves (Allsop et al., 1995 and Franco et al., 1994) give

lower overtopping than steep smooth slopes, but more than a rough rubble mound slope.

The impulsive conditions give a different trend. First of all, the influence of the relative

water depth is fairly small as all curves with different Hm0/hs are quite close. For low

vertical structures (Rc/Hm0 < 1.5) there is hardly any difference between pulsating and

impulsive conditions. The large difference is present for higher vertical structures and

certainly for the very high structures. With impulsive conditions water is thrown high into

the air, which means that overtopping occurs even for very high structures. The vertical

distance that the discharge travels is more or less independent of the actual height of the

structure. For Rc/Hm0 > 3 the curves are almost horizontal.

Another way of comparing various structures is to show the influence of the slope angle

on wave overtopping, and this has been done in Figure 4.2. A vertical structure means

cotα = 0. Steep smooth structures can roughly be described by 1 ≤ cotα ≤ 3. Battered

walls have 0 < cotα < 1. Gentle slopes have roughly cotα ≥ 2 or 3. Figure 4.2 shows

curves for two relative freeboards: Rc/Hm0 = 1.5 & 3.0.

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Of course similar conclusions can be drawn as for the previous comparison. Steep slopes

give the largest overtopping, which reduces for gentler slopes; for a given wave condition

and water level. Vertical slopes give less overtopping than steep smooth slopes, except

for a high vertical structure under impulsive conditions.

Details of all equations used here are described in Chapter 5 (sloping smooth structures),

Chapter 6 (rubble mound structures) and Chapter 7 (vertical structures).

Relative freeboard Rc/Hm0

im en si on le ss o ve rt op pi ng q /(g

m

impulsive vertical Hm0/hs=0.5

impulsive vertical Hm0/hs=0.7

impulsive vertical Hm0/hs=0.9

steep smooth slopes, cota<2

gentle smooth slope, cota=4, so=0.04

steep rubble mound slope, gf=0.5

gentle rubble mound slope, gf=0.5

vertical structure Allsop (1995)

vertical structure Franco et al. (1994)

Figure 4.1: Comparison of wave overtopping formulae for various kind of structures

Slope angle cotα

im en si on le ss o ve rto

pp in g q/ (g

m

vertical, Allsop (1995)

vertical, Franco et al. (1994)

impulsive vertical, Hm0/hs=0.9, so=0.04

smooth slope, so=0.04

smooth slope, so=0.01

Rc/Hm0=3.0

Rc/Hm0=1.5

Figure 4.2: Comparison of wave overtopping as function of slope angle

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4.2.2 Overtopping volumes and Vmax

Wave overtopping is a dynamic and irregular process and the mean overtopping

discharge, q, does not cover this aspect. But by knowing the storm duration, t, and the

number of overtopping waves in that period, Now, it is easy to describe this irregular and

dynamic overtopping, if the overtopping discharge, q, is known. Each overtopping wave

gives a certain overtopping volume of water, V and this can be given as a distribution

As many equations in this manual, the two-parameter Weibull distribution describes the

behaviour quite well. This equation has a shape parameter, b, and a scale parameter, a.

The shape parameter gives a lot of information on the type of distribution. Figure 4.3

gives an overall view of some well-known distributions. The horizontal axis gives the

probability of exceedance and has been plotted according to the Rayleigh distribution.

The reason for this is that waves at deep water have a Rayleigh distribution and every

parameter related to the deep water wave conditions, like shallow water waves or wave

overtopping, directly show the deviation from such a Rayleigh distribution in the graph. A

Rayleigh distribution should be a straight line in Figure 4.3 and a deviation from a straight

line means a deviation from the Rayleigh distribution.

Probability of Exceedance [%]

ve rt op pi ng

ol um e [m 3 /m

b=3

b=2

b=1

b=0.75

b=0.65

b=0.85

Figure 4.3: Various distributions on a Rayleigh scale graph. A straight line (b = 2) is a

Rayleigh distribution

When waves approach shallow water and the highest waves break, the wave distribution

turns into a Weibull distribution with b > 2; also refer to Figure 2.5. An example with b=3

is shown in Figure 4.3 and this indicates that there are more large waves of similar height.

The exponential distribution (often found for extreme wave climates) has b = 1 and shows

that extremes become larger compared to most of the data. Such an exponential

distribution would give a straight line in a log-linear graph.

The distribution of overtopping volumes for all kind of structures have average values

even smaller than b = 1. Such a distribution is even steeper than an exponential

distribution. It means that the wave overtopping process can be described by a lot of fairly

small or limited overtopping volumes and a few very large volumes. The EA-manual

(1999) gives various b-values (and according a-values), based on different and limited

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data sets. The b-values are mostly within the range 0.6 < b < 0.9. For comparison curves

with b = 0.65 and 0.85 are given in Figure 4.3. The curves are very similar, except that

the extremes differ a little. It is for this reason that for smooth slopes an average b-value

of 0.75 was chosen and not different values for various subsets of data. The same

average value has been used for rubble mound structures, which makes smooth and

rubble mound structures easy comparable. The exceedance probability, PV, of an

overtopping volume per wave is then similar to:

exp1

a

with:

owowwm

ov m NtqNNqTP

Equation 4.3 shows that the scale parameter a, depends on the overtopping discharge, q,

but also on the mean period, Tm, and probability of overtopping, Now / Nw, or which is

similar, on the storm duration, t, and the actual number of overtopping waves Nw.

Equations for calculating the overtopping volume per wave for a given probability of

exceedance, is given by Equation 4.2. The maximum overtopping during a certain event

is fairly uncertain, as most maxima, but depends on the duration of the event. In a 6

hours period one may expect a larger maximum than only during 15 minutes. The

maximum overtopping volume by only one wave during an event depends on the actual

number of overtopping waves, Now, and can be calculated by:

( )[ ] 3/4max ln owNaV ⋅= 4.4

Chapters 5, 6 and 7 give formulae for smooth slopes, rubble mound slopes and vertical

walls, respectively. In this Section and example is given between the mean overtopping

discharge, q, and the maximum overtopping volume in the largest wave. Note that the

mean overtopping is given in l/s per m width and that the maximum overtopping volume is

given in l per m width.

As example a smooth slope with slope angle 1:4 is taken, a rubble mound slope with a

steeper slope of 1:1.5 and a vertical wall. The storm duration has been assumed as 2

hours (the peak of the tide) and a fixed wave steepness of s0m-1,0 = 0.04 has been taken.

Figure 4.4 gives the q – Vmax lines for the three structures and for relatively small waves of

Hm0 = 1 m (red lines) and for fairly large waves of Hm0 = 2.5 m (black lines).

A few conclusions can be drawn from Figure 4.4. First of all, the ratio q/Vmax is about 1000

for small q (roughly around 1 l/s per m) and about 100 for large q (roughly around 100 l/s

per m). So, the maximum volume in the largest wave is about 100 – 1000 times larger

than the mean overtopping discharge.

Secondly, the red lines are lower than the black lines, which means that for lower wave

heights, but similar mean discharge, q, the maximum overtopping volume is also smaller.

For example, a vertical structure with a mean discharge of 10 l/s per m gives a maximum

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volume of 1000 l per m for a 1 m wave height and a volume of 4000 l per m for a 2.5 m

wave height.

Finally, the three different structures give different relationships, depending on the

equations to calculate q and the equations to calculate the number of overtopping waves.

More information can be found in Chapters 5, 6 and 7.

Overtopping discharge q [l/s/m]

ax im um v ol um e in o ne w av e [l/

m

Smooth slope Hs=2.5m Rubble mound Hs=2.5m

Vertical Hs=2.5m Smooth slope Hs=1m

Rubble mound Hs=1m Vertical Hs=1m

Figure 4.4: Relationship between mean discharge and maximum overtopping volume in one wave

for smooth, rubble mound and vertical structures for wave heights of 1 m and 2.5 m

4.2.3 Wave transmission by wave overtopping

Admissible overtopping depends on the consequences of this overtopping. If water is

behind a structure, like for breakwaters and low-crested structures along the shore, large

overtopping can be allowed as this overtopping will plunge into the water again. What

happens is that the overtopping waves cause new waves behind the structure. This is

called wave transmission and is defined by the wave transmission coefficient Kt =

Hm0,t/Hm0,i, with Hm0,t = transmitted significant wave height and Hm0,i = incident significant

wave height. The limits of wave transmission are Kt = 0 (no transmission) and 1 (no

reduction in wave height). If a structure has its crest above water the transmission

coefficient will never be larger than about 0.4 - 0.5.

Wave transmission has been investigated in the European DELOS project. For smooth

sloping structures the following prediction formulae were derived:

cos5.0exp175.03.0 βξ ⋅

im

t H

with as a minimum Kt = 0.075 and maximum Kt = 0.8, and limitations 1 < ξop < 3,

0° ≤ β ≤ 70. and 1 < B/Hi < 4, and where β is the angle of wave attack and B is

crest width (and not berm width).

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Figure 4.5 shows the transmission coefficient Kt as a function of the relative freeboard

Rc/Hm0 and for a smooth structure with slope angle cotα = 4 (a gentle smooth low-crested

structure). Three wave steepnesses have been used: s0,p = 0.01 (long waves), 0.03 and

0.05 (short wind waves). Also perpendicular wave attack has been assumed. Wave

transmission decreases for increasing crest height and a longer wave gives more

transmission. Wave overtopping can be calculated for the same structure and wave

conditions, see Chapter 5 and Figure 4.6. Also here a longer wave gives more wave

overtopping.

Rc/Hm0

t so=0.03

so=0.01

so=0.05

Figure 4.5: Wave transmission for a gentle smooth structure of 1:4 and for different wave

steepness

Rc/Hm0

q/ (g

m

so=0.01

so=0.03

so=0.05

Figure 4.6: Wave overtopping for a gentle smooth structure of 1:4 and for different wave

steepness

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The relationship between wave overtopping and transmission is found if both figures are

combined and Figure 4.7 shows this relationship. For convenience the graphs are not

made in a dimensionless way, but for a wave height of 3 m. A very small transmitted

wave height of 0.1 m is only found if the wave overtopping is at least 30 – 50 l/s per m. In

order to reach a transmitted wave height of about 1 m (one-third of the incident wave

height) the wave overtopping should at least be 500 – 2500 l/s/m or 0.5 – 2.5 m3/s/m.

One may conclude that wave transmission is always associated with (very) large wave

overtopping.

Hm0 transmitted [m]

q [l/

s pe r m

so=0.01

so=0.03

so=0.05

Figure 4.7: Wave transmission versus wave overtopping for a smooth 1:4 slope and a

wave height of Hm0 = 3 m.

Wave transmission for rubble mound structures has also been investigated in the

European DELOS project and the following prediction formulae were derived for wave

transmission:

( )( )opmmct HBHRK ξ5.0exp131.064.04.0 00 −−−+−=

for 8.0075.0 ≤≤ tK

Wave overtopping for a rubble mound structure with simple slope can be calculated by

Equations in Chapter 6. A typical rubble mound structure has been used as example, with

cotα = 1.5; 6 – 10 ton rock (Dn50 = 1.5 m) as armour and a crest width of 4.5 m (3 Dn50). A

wave height of 3 m has been assumed with the following wave steepness: s0m-1,0 = 0.01

(long waves), 0.03 and 0.05 (short wind waves). In the calculations the crest height has

been changed to calculate wave transmission as well as wave overtopping.

Figure 4.8 gives the comparison. The graph shows that a longer wave (s0m1,0 = 0.01)

gives more wave transmission, for the same overtopping discharge. The reason could be

that wave overtopping is defined at the rear of the crest, where (without superstructure or

capping wall), waves can penetrate through the armour layer at the crest and generate

waves behind the structure. This is easier for longer waves.

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In contrast to smooth structures, one may conclude that even without considerable wave

overtopping discharge at the rear of the crest, there still might be considerable wave

transmission through the structure. In this example transmitted wave heights between 0.5

m and 1 m are found for overtopping discharges smaller than 100 – 200 l/s per m. Only

larger transmitted wave heights are associated with extreme large overtopping discharges

of more than 500 – 1000 l/s per m.

A simple equation for wave transmission at vertical structures has been given by Goda

03.045.0 mct HRK −= for 25.10 0 << mc HR 4.7

Wave overtopping for a simple vertical structure can be calculated by Equation 7.4. In

both formulae only the relative crest height plays a role and no wave period, steepness or

slope angle. A simple vertical structure has been used as example with a fixed incident

wave height of Hm0 = 3 m. Figure 4.9 gives the comparison of wave overtopping and

wave transmission, where in the calculations the crest height has been changed to

calculate wave transmission as well as wave overtopping.

Hm0 transmitted [m]

q [l/

s pe r m

so=0.01

so=0.03

so=0.05

Figure 4.8: Wave transmission versus wave overtopping discharge for a rubble mound

structure, cotα = 1.5; 6-10 ton rock, B = 4.5 m and Hm0 = 3 m

For comparison the same rubble mound structure has been used as the example in

Figure 4.8, with cotα = 1.5; 6 – 10 ton rock (Dn50 = 1.5 m) as armour, a crest width of

4.5 m (3 Dn50) and a wave steepness s0p = 0.03. The curve for a smooth structure

(Figure 4.7) and for s0p = 0.03 has been given too in Figure 7.24.

A rubble mound structure gives more wave transmission than a smooth structure, under

the condition that the overtopping discharge is similar. But a vertical structure gives even

more transmission. The reason may be that overtopping water over the crest of a vertical

breakwater always falls from a distance into the water, where at a sloping structure water

flows over and/or through the structure.

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One may conclude that even without considerable wave overtopping discharge at the

crest of a vertical structure, there still might be considerable wave transmission. In this

example of a vertical structure, transmitted wave heights between 0.5 m and 1 m are

found for overtopping discharges smaller than 100 – 200 l/s per m.

Hm0 transmitted [m]

q [l/

s pe r m

vertical

rubble mound (s0p=0.03)

smooth (s0p=0.03)

Figure 4.9: Comparison of wave overtopping and transmission for a vertical, rubble mound and

smooth structure

Figure 4.10: Wave overtopping and transmission at breakwater IJmuiden, the Netherlands

The programme PC-OVERTOPPING was made on the results of the Technical TAW Report

“Wave run-up and wave overtopping at dikes” and is used for the 5-yearly safety

assessment of all water defences in the Netherlands. The TAW Report has now in this

Manual been replaced by Chapter 5 (dikes and embankments) and extended for rubble

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mound and vertical structures in Chapters 6 and 7. The programme was mainly based on

a dike type structure. It means that the structure should be sloping, although a small

vertical wall on top of the dike may be taken into account. Also roughness/permeability

different from “smooth” can be taken into account, but not a crest with permeable and

rough rock or armour units. In such a case the structure should be modelled up to the

transition to the crest and other formulae should be used to take into account the effect of

the crest (see Chapter 6).

The programme was set-up in such a way that almost every sloping structure can be

modelled by an unlimited number of sections. Each section is given by x-y coordinates

and each section can have its own roughness factor. The programme calculates almost

all relevant overtopping parameters (except flow velocities and flow depths), such as:

• 2% run-up level;

• mean overtopping discharge;

• percentage of overtopping waves;

• overtopping volumes per wave (maximum and for every percentage defined by the

user);

• required crest height for given mean overtopping discharges (defined by the user).

The main advantages of PC-OVERTOPPING are:

• Modelling of each sloping structure, including different roughness along the slope;

• Calculation of most overtopping parameters, not only the mean discharge.

The main disadvantage is:

• It does not calculate vertical structures and not a rough/permeable crest.

In order to show the capabilities of the programme an example will be given. Figure 4.11

shows the cross-section of a dike with the design water level 1 m above CD. Different

materials are used on the slope: rock, basalt, concrete asphalt, open concrete system and

grass on the upper part of the structure. The structure has been schematised in

Figure 4.12 by x-y coordinates and a selection of the material of the top layer. The

programme selects the right roughness factor.

rock

basalt

concrete

asphalt

open

revetme

nt grass

Figure 4.11: Example cross-section of a dike

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Figure 4.12: Input of geometry by x-y coordinates and choice of top material

Figure 4.13: Input file

The input parameters are the wave height, wave period (choice between the spectral

parameter Tm-1,0 and the peak period Tp), the wave angle, water level (with respect to CD,

the same level as used for the structure geometry) and finally the storm duration and

mean period (for calculation of overtopping volumes, etc.). Figure 4.13 gives the input file.

The output is given in three columns, see Figure 4.14. The left column gives the 2%-runup level, the mean overtopping discharge and the percentage of overtopping waves. If

the 2%-run-up level is higher than the actual dike crest, this level is calculated by

extending the highest section in the cross-section. The middle column gives the required

dike height for given mean overtopping discharges. Also here the highest section is

extended, if required. Finally, in the right column the number of overtopping waves in the

given storm duration are given, together with the maximum overtopping volume and other

volumes, belonging to specified overtopping percentages (percentage of the number of

overtopping waves).

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Figure 4.14: Output of PC-OVERTOPPING

The programme also provides a kind of check whether found results of the 2%-runup level

and mean overtopping discharge fall within measured ranges. All test results where the

formulae were based on, are given in a run-up or overtopping graph, see Figure 4.15 and

Figure 4.16. The graphs show the actual measured run-up or overtopping, including the

effect of reductions due to roughness, berms, etc. The curve gives the maximum, which

means a smooth straight slope with perpendicular wave attack. The programme then

plots the calculated point in these graphs (the green point within the red circle).

Figure 4.15: Check on 2%-runup level

Figure 4.16: Check on mean overtopping discharge

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4.4 Neural network tools

Artificial neural networks fall in the field of artificial intelligence and can in this context be

defined as systems that simulate intelligence by attempting to reproduce the structure of

human brains. Neural networks are organised in the form of layers and within each layer

there are one or more processing elements called ‘neurons’. The first layer is the input

layer and the number of neurons in this layer is equal to the number of input parameters.

The last layer is the output layer and the number of neurons in this layer is equal to the

number of output parameters to be predicted. The layers in between the input and output

layers are the hidden layers and consist of a number of neurons to be defined in the

configuration of the NN. Each neuron in each layer receives information from the

preceding layer through the connections, carries out some standard operations and

produces an output. Each connectivity has a weight factor assigned, as a result of the

calibration of the neural network. The input of a neuron consists of a weighted sum of the

outputs of the preceding layer; the output of a neuron is generated using a linear

activation function. This procedure is followed for each neuron; the output neuron

generates the final prediction of the neural network.

Artificial neural networks have applications in many fields and also in the field of coastal

engineering for prediction of rock stability, forces on walls, wave transmission and wave

overtopping. The development of an artificial neural network is useful if:

• the process to be described is complicated with a lot of parameters involved,

• there is a large amount of data.

Less complicated processes may be described by empirical formulae. This is also true for

the process of wave overtopping, where many formulae exists, but always for a certain

type of structure. Wave overtopping on all kind of structures can not be covered by only

one formula, but a neural network is able to do this. A neural network needs a large

amount of data to become useful for prediction. If the amount of data is too small, many

predictions might be unreliable as the prediction will be out of range. But specially for the

topic of wave overtopping there is an overwhelming amount of tests on all kinds of coastal

structures and embankments.

This was the reason to start the European CLASH project. The result has been that two

neural networks have been developed, one within CLASH and one along side of CLASH

as a PhD-work. In both cases the neural network configuration was based on Figure 4.17,

where the input layer has 15 input parameters (β, h, Hm0toe, Tm-1,0toe, ht, Bt, γf, cotαd, cotαu,

Rc, B, hb, tan αb, Ac, Gc) and 1 output parameter in the output layer (i.e. mean overtopping

discharge, q). CLASH was focused on a three-layered neural network, where a

configuration with one single hidden layer was chosen.

EurOtop Manual

q (m3/s/m)

β h Hm0,toeTm-1,0,toeht Bt γf cotαd cotαu Rc B hb tan αB Ac Gc

Figure 4.17: Configuration of the neural network for wave overtopping

The development of an artificial neural network is a difficult task. All data should be

checked thoroughly (rubbish in = rubbish out) and the training of a neural network needs

special skills. The application of a developed neural network as a prediction tool,

however, is easy and can be done by most practical engineers! It is for this reason that

the CLASH neural network is part of this manual.

The application of the neural network is providing an Excel or ASCII input file with

parameters, run the programme (push a button) and get a result file with mean

overtopping discharge(s). Such an application is as easy as getting an answer from a

formula programmed in Excel and does not need knowledge about neural networks. The

advantages of the neural network are:

• it works for almost every structure configuration,

• it is easy to calculate trends instead of just one calculation with one answer.

The input exists of 10 structural parameters and 4 hydraulic parameters. The hydraulic

parameters are wave height, wave period, and wave angle and water depth just in front of

the structure. The structural parameters describe almost every possible structure

configuration by a toe (2 parameters), two structure slopes (including vertical and wave

return walls), a berm (2 parameters) and a crest configuration (3 parameters). The tenth

structural parameter is the roughness factor for the structure (γf) and describes the

average roughness of the whole structure. Although guidance is given, estimation is not

easy if the structure has different roughness on various parts of the structure. An overall

view of possible structure configurations is shown in Figure 4.18. It clearly shows that the

neural network is able to cope with most structure types.

Very often one is not only interested in one calculation, but in more. As the input file has

no limitations in number of rows (= number of calculations), it is easy to incrementally

increase one or more parameters and to find a trend for a certain (design) measure. As

example for calculation of a trend with the neural network tool an example cross-section of

a rubble mound embankment with a wave wall has been chosen, see Figure 4.19.

EurOtop Manual

If, for example, the cross-section in Figure 4.19 would have too much overtopping, the

following measures could be considered:

• Increasing the crest

• Applying a berm

• Widening the crest

• Increasing only the crest wall

Table 4.1 shows the input file with the first 6 calculations, where incremental increase of

the crest will show the effect of raising the crest on the amount of wave overtopping.

Calculations will give an output file with the mean overtopping discharge q (m3/s per m

width) and with confidence limits. Table 4.2 shows an example which is the output

belonging to the input in Table 4.1.

Table 4.1: Example input file for neural network with first 6 calculations

β h Hm0 Tm-1,0 ht Bt γf cotαd cotαu Rc B hb tanαB Ac Gc

Table 4.2: Output file of neural network with confidence limits

q

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Figure 4.18: Overall view of possible structure configurations for the neural network

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Figure 4.19: Example cross-section with parameters for application of neural network

To make the input file for this example took 1 hour and resulted in 1400 rows or

calculations. The calculation of the neural network took less than 10 seconds. The

results were copied into the Excel input file and a resulting graph was made within Excel,

which took another hour. Figure 4.20 gives the final result, where the four trends are

shown. The base situation had an overtopping discharge of 59 l/s per m. The graph

clearly shows what measures are required to reduce the overtopping by for example a

factor 10 (to 5.9 l/s per m) or to only 1 l/s per m. It also shows that increasing structure

height is most effective, followed by increasing only the crest wall.

Figure 4.20: Results of a trend calculation

Ac; Rc; B or Gc (m)

Overtopping discharge m3

/s/m

Higher structure (Rc, Ac)

Berm at sw (B)

Wider crest (Gc)

Higher wall (Rc)

59 l/s/m

5.9 l/s/m

1 l/s/m

Ac; Rc; B or Gc (m)

ve rt op pi ng d is ch ar ge m 3 /s

/m Higher structure (Rc, Ac)

Berm at sw (B)

Wider crest (Gc)

Higher wall (Rc)

59 l/s/m

5.9 l/s/m

1 l/s/m

H s = 5 m; T p = 10 s β = 0

h = 12 m ht = 9

m B t = 4 m

Xbloc 1:1.5

A c = 5 m

Gc = 5 m

Rc = 4 m

H s = 5 m; T p = 10 s β = 0

h = 12 m ht = 9

m Bt = 4 m

Xbloc 1:1.5

Ac = 5 m

Gc = 5 m

Rc = 4 m

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At present two neural networks exist. One is the official neural network developed by

Delft Hydraulics in the CLASH project. It runs as an executable and can be downloaded

from the CLASH website or the Manual website. The other neural network has also been

developed within CLASH, but as part of a PhD-thesis at Gent University (Verhaeghe,

2005). The network was developed in MatLab® and actually an application can only be

performed if the user has MatLab®, which is not often the case in the engineering world.

An easier application has to be worked out: web based or executable.

The advantage of the Gent neural network is that it first decides whether there will be

overtopping or not (classifier). If there is no overtopping it will give q = 0. If there is

overtopping, it will quantify the overtopping with a similar network as the CLASH network

(quantifier). This is certainly an advantage above the CLASH network. The CLASH

network was only trained with overtopping data (tests with “no overtopping” were not

considered) and, therefore, this network always gives a prediction of overtopping, also in

the range where no overtopping should be expected.

4.5 Use of CLASH database

The EU-programme CLASH resulted in an extensive database with wave overtopping

tests. Each test was described by 31 parameters as hydraulic and structural parameters,

but also parameters describing the reliability and complexity of the test and structure. The

database includes more than 10,000 tests and was set-up as an Excel database. The

database, therefore, is nothing more than a matrix with 31 columns and more than 10,000

rows.

If a user has a specific structure, there is a possibility to look into the database and find

more or less similar structures with measured overtopping discharges. It may even be

possible that the structure has already been tested with the right wave conditions! Finding

the right tests can be done by using filters in the Excel database. Every test of such a

selection can then be studied thoroughly. One example will be described here in depth.

Suppose one is interested in improvement of a vertical wall with a large wave return wall.

The wave conditions are Hm0 toe = 3 m, the wave steepness so = 0.04 (Tm-1,0 = 6.9 s) and

the wave attack is perpendicular to the structure. The design water depth h = 10 m and

the wave return wall starts 1 m above design water level and has a height and width of 2

m (the angle is 45˚ seaward). This gives a crest freeboard Rc = 3 m, equal to the wave

height. Have tests been performed which are close to this specific structure and given

wave conditions?

The first filter selects data with a vertical down slope, i.e. cotαd = 0. The second filter

could select data with a wave return wall overhanging more than about 30° seaward. This

means cotαu < -0.57. In first instance every large wave return wall can be considered, say

at least 0.5Hm0 wide. This gives the third filter, selecting data with -cotαu * (Ac + hb)/Hm0

≥ 0.5. With these 3 filters, the database gives 212 tests from 4 independent test series.

Figure 4.21 shows the data together with the expression of Franco et al. (1994) for a

vertical wall. There are 22 tests without overtopping. They are represented in the figure

with a value of q/(gH3m0toe)½ = 10-7. The majority of the data is situated below the curve for

a vertical wall, indicating that a wave return wall is efficient, but the data is too much

scattered to be decisive.

A next step in the filtering process could be that only wave return walls overhanging more

than 45˚ seaward are selected. This means cotαu < -1. The water depth is relatively large

for the considered case and shallow water conditions are excluded if h/Hm0 toe > 3.

Figure 4.22 shows this further filtering process. The number of data has been reduced to

78 tests from only 2 independent series. In total 12 tests result in no overtopping. The

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data show the trend that the overtopping is in average about ten times smaller than for a

vertical wall, given by the dashed line. But for Rc/Hm0 toe > 1 there are quite some tests

without any overtopping.

Figure 4.21: Overtopping for large wave return walls; first selection

Figure 4.22: Overtopping for large wave return walls; second selection with more criteria

As still quite some data are remaining in Figure 4.22, it is possible to narrow the search

area even further. With a wave steepness of so = 0.04 in the considered case, the wave

steepness range can be limited to 0.03 < so < 0.05. The width of the wave return wall of 2

m gives with the wave height of 3 m a relative width of 0.67. The range can be limited to

0.5 < -cotαu * (Ac + hb)/Hm0 < 0.75. Finally, the transition from vertical to wave return wall

is 1 m above design water level, giving hb/Hm0 toe = -0.33. The range can be set at

-0.5 < hb/Hm0 toe < -0.2.

Rc/Hm0 toe

q/(gH

m0 toe 3 )

series 508

series 914

series 113

series 033

Franco et al.,(1994)

q/

m

Rc/Hm0 toe

q/(gH

m0 toe

series 914

series 113

Franco et al.,(1994)

Rc/Hm0 toe

series 914

series 113

Franco et al.,(1994)

q/

m

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The final selection obtained after filtering is given in Figure 4.23. Only 4 tests remain from

one test series, one test resulted in no overtopping. The data give now a clear picture.

For a relative freeboard lower than about Rc/Hm0 toe = 0.7 the overtopping will not be much

different from the overtopping at a vertical wall. The wave return wall, however, becomes

very efficient for large freeboards and even gives no overtopping for Rc/Hm0 toe > 1.2. For

the structure considered with Rc/Hm0 toe = 1 the wave overtopping will be 20-40 times less

then for a vertical wall and will probably amount to q = 0.5 - 2 l/s per m width. In this

particular case it was possible to find 4 tests in the database with very close similarities to

the considered structure and wave conditions.

Figure 4.23: Overtopping for a wave return wall with so = 0.04, seaward angle of 45˚, a width of 2 m

and a crest height of Rc = 3 m. For Hm0 toe = 3 m the overtopping can be estimated

from Rc/Hm0 toe = 1

4.6 Outline of numerical model types

Empirical models or formulae use relatively simple equations to describe wave

overtopping discharges in relation to defined wave and structure parameters. Empirical

equations and coefficients are, however, limited to a relatively small number of simplified

structure configurations. Their use out of range, or for other structure types, may require

extrapolation, or may indeed not be valid. Numerical models of wave overtopping are less

restrictive, in that any validated numerical model can; in theory; be configured for any

structure within the overall range covered.

Realistic simulations of wave overtopping require numerical methods which are able to

simulate shoaling, breaking on or over the structure, and possible overturning of waves. If

there is violent or substantial wave breaking, or impulsive of waves onto the structure,

then the simulations must be able to continue beyond this point. Wave attack on

permeable coastal structures with a high permeability, such as those consisting of coarse

granular material or large artificial blocks, cannot be modelled without modelling the

porous media flow. The energy dissipation inside the permeable parts, the infiltration and

seepage in the swash and backwash area, and the interactive flow between the external

Rc/Hm0 toe

q/(gH

m0 toe

series 113

Franco et al.,(1994)

q/

m

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wave motion and the internal wave motion often cause the wave attack to be quite

different from the flow on impermeable structures.

All of the processes described above occur during overtopping at structures, and all affect

how the wave overtops and determine the peak and mean discharges. Additionally,

physical model tests suggest that a sea state represented by 1000 random waves will give

reasonably consistent results, but that shorter tests may show significant variations in

extreme statistics. Any numerical model should therefore be capable of running similar

numbers of waves.

There are no numerical models capable of meeting all of the above criteria accurately in a

computationally effective or economical way, and it may be many more years before

advances in computer technology allow these types of models to be used. There are,

however, different model types each capable of meeting some of these criteria. They

essentially fall into two principal categories: the nonlinear shallow water equation models

(NLSW); and those based on the Navier-Stokes equations. Each of these generic types

will now be discussed, with the emphasis on the range of applicability rather than the

underlying mathematical principals.

4.6.1 Navier-Stokes models

The fluid motion for models based on the Navier-Stokes equations will generally be

controlled by one of two principal techniques: the Volume of Fluid (VOF) method first

described by Hirt & Nichols (1981); and the Smooth Particle Hydrodynamics (SPH)

method as discussed by Monaghan (1994). Each of these models requires a detailed

computational grid to be defined throughout the fluid domain, with solutions to the

complex set of equations required at each grid-point before the simulation can continue.

Restricted to only two dimensions, and for computational domains of only two or three

wavelengths, these model types will typically take several minutes of computational time

to simulate small fractions of a second of real time. In general SPH models take longer to

run than VOF models.

An example of a model based on the Navier-Stokes equations is the VOF model SKYLLA.

Developed to provide a wide range of applicability, high accuracy and a detailed

description of the flow field for a wide range of structures, including permeable structures.

It includes combined modelling of free surface wave motion, and porous media flow, and

allows for simulations with large variations in the vertical direction in both the flow field and

in the cross section of the structure. The internal wave motion is simulated within the

porous media flow, and is valid for 2d incompressible flow with constant fluid mass density

through a homogeneous isotropic porous medium. It is, nevertheless, restricted to regular

waves, since irregular waves cannot be computed within manageable computational

times.

Although computationally very expensive, these model types can provide descriptions of

pressure and velocity fields within porous structures, and impulsive and breaking wave

loads. Computation of wave transmission and wave run-up of monochromatic waves is

possible, but the study of more than a few irregular overtopping waves is not yet possible.

4.6.2 Nonlinear shallow water equation models

The one-dimensional shallow water equations were originally developed for near

horizontal, free-surface channel flows. The equations describe water depth and horizontal

velocity in time and space, where vertical velocity is neglected, and only hydrostatic

pressure is considered. The resulting nonlinear shallow water (NLSW) equations; derived

from the Navier-Stokes equations; simplify the mathematical problem considerably,

allowing realistic, but simplified, real-time simulations to be computed.

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The general restriction of these models is that they must be in shallow water (h/L < 0.05) if

the model assumptions are to be preserved, and that waves entering into the

computational domain have or will break. The fundamental mathematical assumption for

NLSW models is that the waves travel as bores as described by Hibberd & Peregrine

(1979). At the crest of a sea defence structure, these models are able to continue

computing as the flows either side of the crest separate, overtop or return.

ODIFLOCS (van Gent, 1994) is a one-dimensional, time-domain model which simulates

the wave attack of perpendicular incident waves on permeable and impermeable coastal

structures. The NLSW model is coupled to an internal porous media flow model

(Kobayashi et al., 1987) that allows homogenous permeable structures to be modelled.

This allows the modelling of infiltration and seepage phenomena, and the internal phreatic

surface can be followed separately from the free surface flow. ODIFLOCS was developed

to estimate permeability coefficients, wave transmission, magnitude of internal set-up, and

the influence of spectral shape on wave run-up and overtopping.

The ANEMONE model suite developed by Dodd (1998), comes as both a 1d and a 2d

plan model, and also incorporates a porous media flow model for examining beaches

(Clarke et al., 2004). The landward boundaries, both for the free surface flow and for the

internal boundary of the porous media flow, can be modelled as open or closed

(non-reflecting or fully reflecting respectively). The model is capable of simulating storms

of a 1000 waves or more at little computational cost, recording wave-by-wave and mean

overtopping discharges.

These models, and others like them, are invaluable tools to examine the difference in

overtopping performance when modifications to a scheme design are to be investigated.

Long wave runs for a variety of sea states, for say a range of crest levels, is a problem

well suited to these models. The overtopping discharges computed by these models

should not, however, be relied upon as this is generally a function of how the model is set

up for a given study: e.g. specification of the position of the seaward boundary in the

model will affect the overtopping rate. The absolute difference in overtopping between

two similar runs will usually produce reliable information.

4.7 Physical modelling

Physical model tests are an established and reliable method for determining mean wave

overtopping discharges for arbitrary coastal structural geometries; additional levels of

sophistication allow individual overtopping volumes to be measured. Typically at Froudian

scales of 1:5 to 1:50, models represent the prototype structure in 2d or 3d, and frequently

occurring and extreme storm events can be modelled. Wave flumes are usually of 0.3 to

1.5 m width with a depth of 0.5 to 1.0 m and fitted with a piston based wave paddle.

Some form of wave absorbing system to compensate for waves reflected from the model

structure is essential for overtopping studies in wave flumes. Wave basin models vary in

size and complexity, and overtopping may often be measured at several locations on the

model.

Physical model tests are particularly useful when assessing wave overtopping, as

overtopping is affected by several factors whose individual and combined influences are

still largely unknown and difficult to predict. The most common hydraulic parameters

which influence wave overtopping are the significant wave height, the wave period, the

wave direction (obliquity), and the water depth at the structure toe. The structural

parameters are the slope, the berm width and level, the crest width and level, and the

geometry of any crest / parapet wall. Where rock or concrete armour are used the

porosity, permeability and placement pattern of armour units affect overtopping as does

the roughness of the individual structural elements.

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Due to the large number of relevant parameters, and the very complex fluid motion at the

structure, theoretical approaches to wave overtopping are not well developed. Physical

model tests, such as wave flume studies, are therefore commonly used to develop

empirical formulae for predicting wave overtopping. These formulae do not assess wave

overtopping discharges and individual volumes accurately, especially for low overtopping

volumes, rather they provide an order of magnitude approximation. This is partially

caused by so far unknown scale and model effects and the fact that only very limited field

data exists. These scale and model effects are briefly discussed in the following section.

There are many cases where there are no reliable empirical overtopping prediction

methods for a given structure geometry, or where the performance of a particular scheme

to reduce overtopping is especially sensitive: e.g. where public safety is a concern.

Alternatively, it may be that the consequences of overtopping are important: e.g. where

overtopping waves cause secondary waves to be generated in the lee of the structure.

For cases such as these, physical model testing may be the only reliable option for

assessing overtopping.

4.8 Model and Scale effects

This section deals with model and scale effects resulting from scaled hydraulic models on

wave overtopping. First, definitions will be given what scale effects and model effects are.

Secondly, a methodology based on the current knowledge is introduced on how to

account for these effects.

4.8.1 Scale effects

Scale effects result from incorrect reproduction of a prototype water-structure interaction

in the scale model. Reliable results can only be expected by fulfilling Froude’s and

Reynolds’ law simultaneously. This is however not possible so that scale effects cannot

be avoided when performing scaled model tests.

Since gravity, pressure and inertial forces are the relevant forces for wave motion most

models are scaled according to Froude’s law. Viscosity forces are governed by Reynolds’

law, elasticity by Cauchy’s law and surface tension forces by Weber’s law, and these

forces have to be neglected for most models. All effects and errors resulting from ignoring

these forces are called scale effects. The problem of the quantification of these scale

effects is still unresolved.

4.8.2 Model and measurement effects

Model or laboratory effects originate from the incorrect reproduction of the prototype

structure, geometry and waves and currents, or due to the boundary conditions of a wave

flume (side walls, wave paddle, etc.). Modelling techniques have developed significantly,

but there are still influences of model effects on hydraulic model results to be expected.

Measurement effects result from different measurement equipment used for sampling the

data in the prototype and model situations. These effects, which are referred to as

“measurement effects” may significantly influence the comparison of results between

prototype and model, or two identical models. It is therefore essential to quantify the

effects and the uncertainty related to the different techniques available.

4.8.3 Methodology

Following the aforementioned definitions the reasons for differences in between model

and prototype data will sometimes be very difficult to assign to either model or scale

effects. During CLASH, the major contributions to model effects were found to be wind

since this is ignored in the hydraulic model. Despite the lack of wind, additional

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differences were found and assigned to be due to model effects. The following

phenomena may give indications of the contributions of the most important model effects

in addition to wind. The repeatability of tests showed that the wave parameters (Hm0, Tp,

Tm-1,0) have a coefficient of variation of CoV~3%, and for wave overtopping the differences

between two wave flumes were CoV~13% and CoV~10%. Different time windows for

wave analysis and different types of wave generation methods had no influence on the

estimated wave parameters (CoV~3%). The number of waves in the flume shows

influence on wave overtopping, where a comparison of 200 compared to 1000 generated

waves show differences in mean overtopping rates up to a value of 20%. The position of

the overtopping tray at the side of the flume showed also differences in overtopping rates

(CoV~20%) from results where the tray was located at the centre of the crest. This could

be because of the different arrangement of the armour units in front of the overtopping

tray or due to the influence of the side walls of the flume. More details on measurements

and model effects are provided by Kortenhaus et al. (2004a).

Scale effects have been investigated by various authors, and this has led to some generic

rules that should be observed for physical model studies. Generally, water depths in the

model should be much larger than h = 2.0 cm, wave periods larger than T = 0.35 s and

wave heights larger than Hs = 5.0 cm to avoid the effects of surface tension; for rubble

mound breakwaters the Reynolds number for the stability of the armour layer should

exceed Re = 3x104; for overtopping of coastal dikes Re > 1x103; and the stone size in the

core of rubble mound breakwaters has to be scaled according to the velocities in the core

rather than the stone dimensions, especially for small models. The method for how this

can be achieved is given in Burcharth et al. (1999). Furthermore, critical limits for the

influence of viscosity and surface tension are given in Table 4.3, more details can be

found in Schüttrumpf and Oumeraci (2005).

Table 4.3: Scale effects and critical limits

Process Relevant forces Similitude law Critical limits

Wave propagation

Gravity force

Friction forces

Surface tension

FrW,

ReW,

We ReW > ReW,crit = 1x104

T > 0,35 s; h > 2,0 cm

Wave breaking

Gravity force

Friction forces

Surface tension

FrW,

ReW,

We ReW > ReW,crit = 1x104

T > 0,35 s; h > 2,0 cm

Wave run-up

Gravity force

Friction forces

Surface tension

FrA, Frq

Req,

We Req > Req,crit = 103

We > Wecrit = 10

Wave overtopping

Gravity force

Friction forces

Surface tension

FrA , Frq,

Req,

We Req > Req,crit = 103

We > Wecrit = 10

With: FrW=c/(g.h)1/2; FrA=vA/(g.hA)1/2; Frq=vA/(2.g.Ru); ReW = c.h/ν; Req=(Ru-RC)2/(ν.T));

We=vA.hA.ρW/σW

From observations in prototype and scaled models, a methodology was derived to

account for those differences without specifically defining which model and measurement

effects contribute how much. These recommendations are given in subsections 5.7 for

dikes, 6.3.6 for rubble slopes, and 7.3.6 and 7.3.7 for vertical walls, respectively.

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4.9 Uncertainties in predictions

Sections 4.2 to 4.4 have proposed various models to predict wave overtopping of coastal

structures. These models will now be discussed with regard to their uncertainties.

4.9.1 Empirical Models

It has been discussed in section 1.5.4 that the model uncertainty concept uses a mean

factor of 1.0 and a Gaussian distribution around the mean prediction. The standard

deviation is derived from the comparison of model data and the model prediction.

This has two implications for design: Probabilistic design values for all empirical models

used in this manual describe the mean approach for all underlying data points. This

means that, for normally distributed variables, about 50% of the data points exceed the

prediction by the model, and 50% are below the predicted values. This value should be

used if probabilistic design methods are used.

The deterministic design value for all models will be given as the mean value plus one

standard deviation, which in general gives a safer approach, and takes into account that

model uncertainty for wave overtopping is always significant.

4.9.2 Neural Network

When running the Neural Network model the user will be provided with wave overtopping

ratios based on the CLASH database and the Neural Network prediction (Section 4.4).

Together with these results the user will also obtain the uncertainties of the prediction

through the 5% and 95% confidence intervals.

Assuming a normal distribution of the results will allow an estimate of the standard

deviation of the overtopping ratio and hence the whole Gaussian distribution. Results

from the Neural Network prediction can then be converted to the methodology referenced

in Section 4.8 by providing all other confidence intervals and exceedance probabilities

required there. Details will be given when test cases will be investigated.

4.9.3 CLASH database

The CLASH database is described in Section 4.5. It provides a large dataset of available

model data on wave overtopping of coastal structures. It should be mentioned that the

model and scale effects approach introduced in Section 4.8 has not been applied to the

database. Whenever these data are used for prototype predictions the user will have to

check whether any scaling correction procedure is needed.

With respect to uncertainties all model results will contain variations in the measured

overtopping ratios. Most of these variations will result from measurement and model

effects as discussed earlier. Since the database is no real model but an additional source

of data information no model uncertainty can be applied.

4.10 Guidance on use of methods

This manual is accompanied by an overall Calculation Tool outlined in Appendix A. This

tool includes the elements:

• Empirical Calculator programmed with the main empirical overtopping equations

in Chapters 5, 6 and 7 (limited to those that can be described explicitly, that is

without iteration).

• PC-Overtopping, which codes all the prediction methods presented in Chapter 5

for mean overtopping discharge for (generally shallow sloped) sea dikes, see

section 4.3.

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• Neural Network tool developed in the CLASH research project to calculate mean

overtopping for many types of structures, see section 4.4.

• CLASH database, a listing of input parameters and mean overtopping discharge

from each of approximately 10,000 physical model tests on both idealised

(research) test structures, and site specific designs. These data can be sifted to

identify test results that may apply for configurations close to the reader’s, see

section 4.5.

None of these methods give the universally ‘best’ results. The most reliable method to be

used will depend on the type and complexity of the structures, and the closeness with

which it conforms to simplifying assumptions used in previous model testing (on which all

of the methods above are inherently based).

In selecting which method to use, or which set of results to prefer when using more than

one method, the user will need to take account of the origins of each method. It may also

be important in some circumstances to use an alternative method to give a check on a

particular set of calculations. To assist these judgements, a set of simple rules of thumb

are given here, but as ever, these should not be treated as universal truths.

• For simple vertical, composite, or battered walls which conform closely to the

idealisations in Chapter 7, the results of the Empirical Calculator are likely to be

more reliable than the other methods as test data for these structure types do not

feature strongly in the Database or Neural Network, and PC-Overtopping is not

applicable.

• For simple sloped dikes with a single roughness, many test data have been used

to develop the formulae in the Empirical Calculator, so this may be the most

reliable, and simplest to use / check. For dikes with multiple slopes or roughness,

PC-Overtopping is likely to be the most reliable, and easiest to use, although

independent checking may be more complicated. The Database or Neural

Network methods may become more reliable where the structure starts to include

further elements.

• For armoured slopes and mounds, open mound structures that most closely

conform to the simplifying models may best be described by the formulae in the

Empirical Calculator. Structures of lower permeability may be modelled using

PC-Overtopping. Mounds and slopes with crown walls may be best represented

by application of the Database or Neural Network methods.

• For unusual or complex structures with multiple elements, mean overtopping

discharge may be most reliably predicted by PC-Overtopping (if applicable) or by

the Database or Neural Network methods.

• For structures that require use of the Neural Network method, it is possible that the

use of many data for other configurations to develop a single Neural Network

method may introduce some averaging. It may therefore be appropriate to check

in the Database to see whether there are already test data close to the

configuration being considered. This procedure may require some familiarity with

manipulating these types of test data.

In almost all instances, the use of any of these methods will involve some degree of

simplification of the true situation. The further that the structure or design (analysis)

conditions depart from the idealised configurations tested to generate the methods / tools

discussed, the wider will be the uncertainties. Where the importance is high of the assets

being defended, and/or the uncertainties in using these methods are large, then the

design solution may require use of site specific physical model tests, as discussed in

section 4.6.

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5.1 Introduction

An exact mathematical description of the wave run-up and wave overtopping process for

coastal dikes or embankment seawalls is not possible due to the stochastic nature of

wave breaking and wave run-up and the various factors influencing the wave run-up and

wave overtopping process. Therefore, wave run-up and wave overtopping for coastal

dikes and embankment seawalls are mainly determined by empirical formulas derived

from experimental investigations. The influence of roughness elements, wave walls,

berms, etc. is taken into account by introducing influence factors. Thus, the following

chapter is structured as follows.

Figure 5.1: Wave run-up and wave overtopping for coastal dikes and embankment seawalls:

definition sketch. See Section 1.4 for definitions.

First, wave run-up will be described as a function of the wave breaking process on the

seaward slope for simple smooth and straight slopes. Then, wave overtopping is

discussed with respect to average overtopping discharges and individual overtopping

volumes. The influencing factors on wave run-up and wave overtopping like berms,

roughness elements, wave walls and oblique wave attack are handled in the following

section. Finally, the overtopping flow depth and the overtopping flow velocities are

discussed as the direct influencing parameters to the surface of the structure. The main

calculation procedure for coastal dikes and embankment seawalls is given in Figure 5.2.

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Figure 5.2: Main calculation procedure for coastal dikes and embankment seawalls

Definitions of, and detailed descriptions of, wave run-up, wave overtopping, foreshore,

structure, slope, berm and crest height are given in Section 1.4 and are not repeated here.

5.2 Wave run-up

The wave run-up height is defined as the vertical difference between the highest point of

wave run-up and the still water level (SWL) (Figure 5.3). Due to the stochastic nature of

the incoming waves, each wave will give a different run-up level. In the Netherlands as

well as in Germany many dike heights have been designed to a wave run-up height Ru2%.

This is the wave run-up height which is exceeded by 2% of the number of incoming waves

at the toe of the structure. The idea behind this was that if only 2% of the waves reach the

crest of a dike or embankment during design conditions, the crest and inner slope do not

need specific protection measures other than clay with grass. It is for this reason that

much research in the past has been focused on the 2%-wave run-up height. In the past

decade the design or safety assessment has been changed to allowable overtopping

instead of wave run-up. Still a good prediction of wave run-up is valuable as it is the basic

input for calculation of number of overtopping waves over a dike, which is required to

calculate overtopping volumes, overtopping velocities and flow depths.

The general formula that can be applied for the 2%-wave run-up height is given by

Equation 5.1: The relative wave run-up height Ru,2%/Hm0 in Equation 5.11 is related to the

breaker parameter ξm-1,0. The breaker parameter or surf similarity parameter ξm-1,0 relates

the slope steepness tan α (or 1/n) to the wave steepness sm-1,0 = Hm0/L0 and is often used

to distinguish different breaker types, see Section 1.4.

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m u c

R ξγγγ β with a maximum of

m f m u cc

where:

Ru2% = wave run-up height exceeded by 2% of the incoming waves [m]

c1,c2 and c3 = empirical coefficients [-] with

tr tr ccc

γb = influence factor for a berm [-]

γf = influence factor for roughness elements on a slope [-]

γβ = influence factor for oblique wave attack [-]

ξm-1,0 = breaker parameter = ( ) 5.00,1/tan −msα [-]

ξtr = transition breaker parameter between breaking and non-breaking

waves (refer to Section 1.4.3)

The relative wave run-up height increases linearly with increasing ξm-1,0 in the range of

breaking waves and small breaker parameters less than ξtr. For non-breaking waves and

higher breaker parameter than ξtr the increase is less steep as shown in Figure 5.4 and

becomes more or less horizontal. The relative wave run-up height Ru,2%/Hm0 is also

influenced by: the geometry of the coastal dike or embankment seawall; the effect of wind;

and the properties of the incoming waves.

Figure 5.3: Definition of the wave run-up height Ru2% on a smooth impermeable slope

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Figure 5.4: Relative Wave run-up height Ru2%/Hm0 as a function of the breaker parameter ξm-1,0, for

smooth straight slopes

Figure 5.5: Relative Wave run-up height Ru2%/Hm0 as a function of the wave steepness for smooth

straight slopes

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The geometry of the coastal dike is considered by the slope tan α, the influence factor for

a berm γb, the influence factor for a wave wall γV and the influence factor for roughness

elements on the slope γf. These factors will be discussed in Sections 5.3.2, 5.3.4 and

The effect of wind on the wave run-up-height for smooth impermeable slopes will mainly

be focused on the thin layer in the upper part of the run-up. As described in Section 1.4,

very thin layers of wave run-up are not considered and the run-up height was defined

where the run-up layer becomes less than 1-2 cm. Wind will not have a lot of effect then.

This was also proven in the European programme OPTICREST, where wave run-up on

an actual smooth dike was compared with small scale laboratory measurements. Scale

and wind effects were not found in those tests. It is recommended not to consider the

influence of wind on wave run-up for coastal dikes or embankment seawalls.

The properties of the incoming waves are considered in the breaker parameter ξm-1,0 and

the influence factor for oblique wave attack γβ which is discussed in Section 5.3.3. As

given in Section 1.4, the spectral wave period Tm-1,0 is most suitable for the calculation of

the wave run-up height for complex spectral shapes as well as for theoretical wave

spectra (JONSWAP, TMA, etc.). This spectral period Tm-1,0 gives more weight to the

longer wave periods in the spectrum and is therefore well suited for all kind of wave

spectra including bi-modal and multi-peak wave spectra. The peak period Tp, which was

used in former investigations, is difficult to apply in the case of bi-modal spectra and

should not be applied for multi peak or flat wave spectra as this may lead to large

inaccuracies. Nevertheless, the peak period Tp is still in use for single peak wave spectra

and there is a clear relationship between the spectral period Tm-1,0 and the peak period Tp

for traditional single peak wave spectra:

0,11.1 −= mp TT 5.2

Similar relationships exist for theoretical wave spectra between Tm-1,0 and other period

parameters like Tm and Tm0,1, see Section 1.4. As described in Section 1.4, it is

recommended to use the spectral wave height Hm0 for wave run-up height calculations.

The recommended formula for wave run-up height calculations is based on a large

(international) dataset. Due to the large dataset for all kind of sloping structures a

significant scatter is present, which cannot be neglected for application. There are several

ways to include this uncertainty for application, but all are based on the formula describing

the mean and a description of the uncertainty around this mean. This formula is given first

and then three kinds of application: deterministic design or safety assessment;

probabilistic design; and prediction or comparison with measurements. The formula is

valid in the area of 0.5 < γb·ξm-1,0 ≤ 8 to 10.

The formula of wave run-up is given by Equation 5.3 and by the solid line in Figure 5.6

which indicates the average value of the 2% measured wave run-up heights.

m u

with a maximum of

m fb m u

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Figure 5.4 shows the influence of the wave steepness for different slopes on the

dimensionless wave run-up height Ru2%/Hm0.

The wave run-up formulas are given in Figure 5.6 together with measured data from small

and large scale model tests. All data were measured under perpendicular wave attack

and in relatively deep water at the dike toe without any significant wave breaking in front

of the dike toe.

m u

mm u

Figure 5.6: Wave run-up for smooth and straight slopes

The statistical distribution around the average wave run-up height is described by a

normal distribution with a variation coefficient σ’ = σ / μ = 0.07. It is this uncertainty which

should be included in application of the formula. Exceedance lines, for example, can be

drawn by using Ru2% / Hm0 = μ ± x · σ = μ ± x · σ’ · μ, where μ is the prediction by

Equation 5.3, σ = σ’ · μ the standard deviation, and x a factor of exceedance percentage

according to the normal distribution. For example x = 1.64 for the 5% exceedance limits

and x = 1.96 for the 2.5% exceedance limits. The 5% upper exceedance limit is also

given in Figure 5.6.

m u

R ξγγγ β with a maximum of

m f m u

Deterministic design or safety assessment: For design or a safety assessment of the

crest height, it is advised not to follow the average trend, but to include the uncertainty of

the prediction. In many international standards and guidelines a safety margin of about

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one standard deviation is used in formulae where the formula itself has significant scatter.

Note that this standard deviation does not take into account the uncertainty of the

parameters used, like the wave height and period. The equation for deterministic

calculations is given by the dashed line in Figure 5.7 together with the equation for

probabilistic design. Equation 5.4 is recommended for deterministic calculations.

Figure 5.7: Wave run-up for deterministic and probabilistic design

Probabilistic design: Besides deterministic calculations, probabilistic calculations can

be made to include the effect of uncertainties of all parameters or to find optimum levels

including the wind, wave and surge statistics. For probabilistic calculations Equation 5.3

is used together with the normal distribution and variation coefficient of σ’ = 0.07.

Prediction or comparison of measurements: The wave run-up equation can also be

used to predict a measurement in a laboratory (or in real situations) or to compare with

measurements performed. In that case Equation 5.3 for the average wave run-up height

should be used, preferably with for instance the 5% upper and lower exceedance lines.

The influence factors γb, γf and γβ where derived from experimental investigations. A

combination of influence factors is often required in practice which reduces wave run-up

and wave overtopping significantly. Systematic investigations on the combined influence

of wave obliquity and berms showed that both influence factors can be used

independently without any interactions. Nevertheless, a systematic combination over the

range of all influence factors and all combinations was not possible until now. Therefore,

further research is recommended if the overall influence factor γb γf γβ becomes lower

than 0.4.

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5.2.1 History of the 2% value for wave run-up

The choice for 2% has been made long ago and was probably arbitrary. The first

international paper on wave run-up, mentioning the 2% wave run-up, is Asbeck et al.,

1953. The formula Ru2% = 8 Hm0 tanα has been mentioned there (for 5% wave steepness

and gentle smooth slopes, and this formula has been used for the design of dikes till

1980. But the choice for the 2% was already made there.

The origin stems from the closing of the Southern Sea in the Netherlands in 1932 by the

construction of a 32 km long dike (Afsluitdijk). This created the fresh water lake

IJsselmeer and in the 45 years after closure about half of the lake was reclaimed as new

land, called polders. The dikes for the first reclamation (North East Polder) had to be

designed in 1936/1937. It is for this reason that in 1935 en 1936 a new wind-wave flume

was built at Delft Hydraulics and first tests on wave run-up were performed in 1936. The

final report on measurements (report M101), however, was issued in 1941 “due to lack of

time”. But the measurements had been analysed in 1936 to such a degree that “the

dimensions of the dikes of the North East Polder could be established”. That report could

not be retrieved from Delft Hydraulics’ library. The M101 report gives only the 2% wave

run-up value and this must have been the time that this value would be the right one to

design the crest height of dikes.

Further tests from 1939 – 1941 on wave run-up, published in report M151 in 1941,

however, used only the 1% wave run-up value. Other and later tests (M422, 1953; M500,

1956 and M544, 1957) report the 2%-value, but for completeness give also the 1%, 10%,

20% and 50%.

It can be concluded that the choice for the 2% value was made in 1936, but the reason

why is not clear as the design report itself could not be retrieved.

5.3 Wave overtopping discharges

5.3.1 Simple slopes

Wave overtopping occurs if the crest level of the dike or embankment seawall is lower

than the highest wave run-up level Rmax. In that case, the freeboard RC defined as the

vertical difference between the still water level (SWL) and the crest height becomes

important (Figure 5.3). Wave overtopping depends on the freeboard RC and increases for

decreasing freeboard height RC. Usually wave overtopping for dikes or coastal

embankments is described by an average wave overtopping discharge q, which is given in

m3/s per m width, or in litres/s per m width.

An average overtopping discharge q can only be calculated for quasi-stationary wave and

water level conditions. If the amount of water overtopping a structure during a storm is

required, the average overtopping discharge has to be calculated for each more or less

constant storm water level and constant wave conditions.

Many model studies were performed to investigate the average overtopping discharge for

specific dike geometries or wave conditions. For practical purposes, empirical formulae

were fitted through experimental model data which obey often one of the following

expressions:

( ) ( )*0**0* expor 1 RbQQRQQ b ⋅−=−= 5.5

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Q* is a dimensionless overtopping discharge, R* is a dimensionless freeboard height, Q0

describes wave overtopping for zero freeboard and b is a coefficient which describes the

specific behaviour of wave overtopping for a certain structure. Schüttrumpf (2001)

summarised expressions for the dimensionless overtopping discharge Q* and the

dimensionless freeboard height R*.

As mentioned before, the average wave overtopping discharge q depends on the ratio

between the freeboard height RC and the wave run-up height Ru:

u

The wave run-up height Ru can be written in a similar expression as the wave run-up

height Ru,2% giving the following relative freeboard height:

vfbmmu

Hc

for breaking waves and a maximum of

Hc

for non-breaking waves

The relative freeboard does not depend on the breaker parameter ξm-1,0 for non breaking

waves (Figure 5.8), as the line is horizontal.

Figure 5.8: Wave overtopping as a function of the wave steepness Hm0/L0 and the slope

The dimensionless overtopping discharge Q* = q/(gH3m0)½ is a function of the wave height,

originally derived from the weir formula.

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Probabilistic design and prediction or comparison of measurements (ξm-1,0<5): TAW

(2002) used these dimensionless factors to derive the following overtopping formulae for

breaking and non-breaking waves, which describe the average overtopping discharge:

vfbmm

mb m

Hg q

75.4exp

tan

with a maximum of: ⎟

m

Hg q

6.2exp2.0

The reliability of Equation 5.8 is described by taking the coefficients 4.75 and 2.6 as

normally distributed stochastic parameters with means of 4.75 and 2.6 and standard

deviations σ = 0.5 and 0.35 respectively. For probabilistic calculations Equation 5.8

should be taken together with these stochastic coefficients. For predictions of

measurements or comparison with measurements also Equation 5.8 should be taken with,

for instance, 5% upper and lower exceedance curves.

Equation 5.8 is given in Figure 5.9 together with measured data for breaking waves from

different model tests in small and large scale as well as in wave flumes and wave basins.

In addition, the 5% lower and upper confidence limits are plotted.

Figure 5.9: Wave overtopping data for breaking waves and overtopping Equation 5.8 with 5%

under and upper exceedance limits

Data for non-breaking waves are presented in Figure 5.10 together with measured data,

the overtopping formula for non-breaking waves and the 5% lower and upper confidence

limits.

Equation 5.8 gives the averages of the measured data and can be used for probabilistic

calculations or predictions and comparisons with measurements.

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Deterministic design or safety assessment (ξm-1,0<5): For deterministic calculations in

design or safety assessment it is strongly recommended to increase the average

discharge by about one standard deviation. Thus, Equation 5.9 should be used for

deterministic calculations in design and safety assessment:

vfbmm

mb m

Hg q

3.4exp

tan

with a maximum of: ⎟

m

Hg q

3.2exp2.0

A comparison of the two recommended formulas for deterministic design and safety

assessment (Equation 5.8) and probabilistic calculations (Equation 5.9) for breaking and

non-breaking waves is given in Figure 5.11 and Figure 5.12.

In the case of very heavy breaking on a shallow foreshore the wave spectrum is often

transformed in a flat spectrum with no significant peak. In that case, long waves are

present and influencing the breaker parameter ξm-1,0. Other wave overtopping formulas

(equation 5.10 and 5.11) are recommended for shallow and very shallow foreshores to

avoid a large underestimation of wave overtopping by using formulas 5.8 and 5.9. Since

formulas 5.8 and 5.9 are valid for breaker parameters ξm-1,0<5 a linear interpolation is

recommended for breaker parameters 5<ξm-1,0<7.

Figure 5.10: Wave overtopping data for non-breaking waves and overtopping Equation 5.9 with 5%

under and upper exceedance limits

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Figure 5.11: Wave overtopping for breaking waves – Comparison of formulae for design and safety

assessment and probabilistic calculations

Figure 5.12: Wave overtopping for non-breaking waves – Comparison of formulae for design and

safety assessment and probabilistic calculations

Deterministic design or safety assessment (ξm-1,0>7): The following formula is

recommended including a safety margin for deterministic design and safety assessment.

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exp21.0

0 mmf

m

Hg q

Probabilistic design and prediction or comparison of measurements (ξm-1,0>7): The

following formula was derived from measurements with a mean of -0.92 and a standard

deviation of 0.24:

exp10

0 mmf

Cc m

Hg q

British guidelines recommend a slightly different formula to calculate wave overtopping

for smooth slopes, which was originally developed by Owen (1980) for smooth sloping

and bermed seawalls:

Sm HgT

bQ HgT

q exp0 5.12

where Q0 and b are empirically derived coefficients given in Table 5.1 (for straight slopes

only).

Table 5.1: Owen’s coefficients for simple slopes

Seawall Slope Q0 b

Equation 5.2 uses the mean period Tm instead of the spectral wave period Tm-1,0 and has

therefore the limitation of normal single peaked spectra which are not too wide or too

narrow. Furthermore Hs, being H1/3, was used and not Hm0, although this only makes a

difference in shallow water. Equation 5.12 looks quite different to 5.8 and 5.9, but actually

can be rewritten to a shape close to the breaking wave part of these formulae:

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m s sH

bsQ

Hg q

exp/ 5.13

If now tanα would be introduced in Equation 5.12 with a fit to the coefficients in Table 5.1,

a similar formula as the breaking wave Equation 5.9 would be found. One restriction is

that Equation 5.12 has no maximum for breaking waves, which may lead to significant

over predictions for steep slopes and long waves.

The original data of Owen (1980) were also used to develop Equations 5.8 and 5.9, which

avoids the interpolation effort of the Owen formula for different slope angles given in

Table 5.1 and overcomes other restrictions described above. But there is no reason not

to use Equation 5.12 within the limits of application.

Zero Freeboard: Wave overtopping for zero freeboard (Figure 5.13) becomes important

if a dike or embankment seawall is overtopping resistant (for example a low dike of

asphalt) and the water level comes close to the crest. Schüttrumpf (2001) performed

model tests for different straight and smooth slopes in between 1:3 and 1:6 to investigate

wave overtopping for zero freeboard and derived the following formula (σ’ = 0.14), which

should be used for probabilistic design and prediction and comparison of measurements

(Figure 5.14):

m mHg

q ξ for: ξm-1,0 < 2.0

mmHg

q

for: ξm-1,0 ≥ 2.0

For deterministic design or safety assessment it is recommended to increase the average

overtopping discharge in Equation 5.14 by about one standard deviation.

Negative freeboard: If the water level is higher than the crest of the dike or embankment

seawall, large overtopping quantities overflow/overtop the structure. In this situation, the

amount of water flowing to the landward side of the structure is composed by a part which

can be attributed to overflow (qoverflow) and a part which can be attributed to overtopping

(qovertop). The part of overflowing water can be calculated by the well known weir formula

for a broad crested structure:

36.0 Coverflow Rgq −⋅⋅= 5.15

where RC is the (negative) relative crest height and –Rc is the overflow depth [m]

The effect of wave overtopping (qovertop) is accounted for by the overtopping discharge at

zero freeboard (RC=0) in Equation 5.14 as a first guess.

The effect of combined wave run-up and wave overtopping is given by the superposition

of overflow and wave overtopping as a rough approximation:

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36.0 Covertopoverflow Rgqqq −⋅⋅=+= +

00,10537.0 mm Hg ⋅⋅⋅ −ξ

for: ξm-1,0 < 2.0

Wave overtopping is getting less important for increasing overflow depth RC. An

experimental verification of Equation 5.16 is still missing. Therefore, no distinction was

made here for probabilistic and deterministic design.

Figure 5.13: Dimensionless overtopping discharge for zero freeboard (Schüttrumpf, 2001)

(a) Wave overtopping for positive freeboard (b) Wave overtopping for zero freeboard

(c) Overflow for negative freeboard (d) Overflow and overtopping for

negative freeboard

Figure 5.14: Wave overtopping and overflow for positive, zero and negative freeboard

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5.3.2 Effect of roughness

Most of the seadikes and embankment seawalls are on the seaward side covered either

by grass (Figure 5.15), by asphalt (Figure 5.16) or by concrete or natural block revetment

systems (Figure 5.17). Therefore, these types of surface roughness (described as

smooth slopes) were often used as reference in hydraulic model investigations and the

influence factor for surface roughness γf of these smooth slopes for wave heights greater

than about 0.75 m is equal to γf = 1.0.

Figure 5.15: Dike covered by grass (photo: Schüttrumpf)

Figure 5.16: Dike covered by asphalt (photo: Schüttrumpf)

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Figure 5.17: Dike covered by natural bloc revetment (photo: Schüttrumpf)

For significant wave heights Hs less than 0.75 m, grass influences the run-up process and

lower influence factors γf are recommended by TAW (1997) (Figure 5.18). This is due to

the relatively greater hydraulic roughness of the grass surface for thin wave run-up

depths.

5.015.1 Sf H=γ for grass and HS < 0.75m 5.17

Wave height HS [m]

In flu

en ce fa ct or fo r g

ra ss s ur fa ce

f [

Grass

Figure 5.18: Influence factor for grass surface

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Roughness elements (Figure 5.19) or slopes partly covered by rock are often used to

increase the surface roughness and to reduce the wave run-up height and the wave

overtopping rate. Roughness elements are either used to influence the wave run-up or

the wave run-down process. Figure 5.21 shows the influence of artificial roughness

elements on the wave run-up and run-down process. Roughness elements are applied

either across the entire slope or for parts of the slope which should be considered during

the calculation process.

Figure 5.19: Example for roughness elements (photo: Schüttrumpf)

Available data on the influence of surface roughness on wave run-up and wave

overtopping are based on model tests in small, but mainly in large scale, in order to avoid

scale effects. A summary of typical types of surface roughness is given in Table 5.2.

The influence factors for roughness elements apply for γb·ξm-1,0<1.8, increase linearly up to

1.0 for γb·ξm-1,0=10 and remain constant for greater values. The efficiency of artificial

roughness elements such as blocks or ribs depends on the width of the block or rib fb, the

height of the blocks fh and the distance between the ribs fL. The optimal ratio between the

height and the width of the blocks was found to be fh/fb = 5 to 8 and the optimal distance

between ribs is fL/fb = 7. When the total surface is covered by blocks or ribs and when the

height is at least fh/Hm0 = 0.15, then the following minimum influence factors are found:

Block, 1/25 of total surface covered γf,min = 0.85

Block, 1/9 of total surface covered γf,min = 0.80

Ribs, fL/fb = 7 apart (optimal) γf,min = 0.75

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Table 5.2: Surface roughness factors for typical elements

Reference type γf

Concrete 1.0

Asphalt 1.0

Closed concrete blocks 1.0

Grass 1.0

Basalt 0.90

Small blocks over 1/25 of surface 0.85

Small blocks over 1/9 of surface 0.80

¼ of stone setting 10 cm higher 0.90

Ribs (optimum dimensions) 0.75

fb fh fL Figure 5.20: Dimensions of roughness elements

A greater block or rib height than fh/Hm0 = 0.15 has no further reducing effect. If the height

is less, then an interpolation is required:

min, 15.0

m h ff H

fγγ for: fh/Hm0 < 0,15 5.18

As already mentioned, roughness elements are mostly applied for parts of the slope.

Therefore, a reduction factor is required which takes only this part of the slope into

account.

It can be shown that roughness elements have no or little effect below 0.25·Ru2%,smooth

below the still water line and above 0.50·Ru2%,smooth above the still water line. The resulting

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influence factor γf is calculated by weighting the various influence factors γf,i and by

including the lengths Li of the appropriate sections i in between SWL-0.25·Ru2%smooth and

SWL+0.50·Ru2%smooth:

= n

i i n i iif

f

It appears that roughness elements applied only under water (with a smooth upper slope)

have no effect and, in such a case, should be considered as a smooth slope. For

construction purposes, it is recommended to restrict roughness elements to their area of

influence. The construction costs will be less than covering the entire slope by roughness

elements.

The effect of roughness elements on wave run-up may be reduced by debris between the

elements.

Figure 5.21: Performance of roughness elements showing the degree of turbulence

5.3.3 Effect of oblique waves

Wave run-up and wave overtopping can be assumed to be equally distributed along the

longitudinal axis of a dike. If this axis is curved, wave run-up or wave overtopping will

certainly increase for concave curves; with respect to the seaward face; due to the

accumulation of wave run-up energy. Similarly, wave run-up and overtopping will

decrease for convex curves, due to the distribution of wave run-up energy. No

experimental investigations are known concerning the influence of a curved dike axis and

the spatial distribution of wave run-up and wave overtopping yet.

Only limited research is available on the influence of oblique wave attack on wave run-up

and wave overtopping due to the complexity and the high costs of model tests in wave

basins. Most of the relevant research was performed on the influence of long crested

waves and only few investigations are available on the influence of short crested waves

on wave run-up and wave overtopping. Long crested waves have no directional

distribution and wave crests are parallel and of infinite width. Only swell coming from the

ocean can be regarded as a long crested wave. In nature, storm waves are short crested

(Figure 5.23). This means, that wave crests are not parallel, the direction of the individual

waves is scattered around the main direction and the crests of the waves have a finite

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width. The directional spreading might be characterized by the directional spreading width

σ or the spreading factor s. Relations between these parameters are approximately:

σ−=s or:

s

The directional spreading width is σ = 0° (s = ∞) for long crested waves. Results of

systematic research on the influence of oblique wave attack on wave run-up and wave

overtopping under short crested wave conditions are summarized in EAK (2002) and TAW

(2002). The data of this systematic research were summarized in Figure 5.24. Data for

long crested waves are not presented here.

The angle of wave attack β is defined at the toe of the structure after any transformation

on the foreshore by refraction or diffraction as the angle between the direction of the

waves and the perpendicular to the long axis of the dike or revetment as shown in

Figure 5.22. Thus, the direction of wave crests approaching parallel to the dike axis is

defined as β = 0° (perpendicular wave attack). The influence of the wave direction on

wave run-up or wave overtopping is defined by an influence factor γβ:

u u

for wave run-up 5.21

q for wave overtopping 5.22

Wave crests

Dike

Figure 5.22: Definition of angle of wave attack β

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Figure 5.23: Short crested waves resulting in wave run-up and wave overtopping (photo: Zitscher)

For practical purposes, it is recommended to use the following expressions for short

crested waves to calculate the influence factor γβ for wave run-up:

°≤≤°−= 80 0:for 0022.01 ββγ β

°>= 80 :for 824.0 βγ β

and wave overtopping:

°≤≤°−= 80 0:for 0033.01 ββγ β

°>= 80 :for 736.0 βγ β

New model tests (Schüttrumpf et al. (2003)) indicate that formulae 5.21 and 5.22

overestimate slightly the reduction of wave run-up and wave overtopping for small angles

of wave attack. The influence of wave direction on wave run-up or wave overtopping can

be even neglected for wave directions less than |β| = 20°.

For wave directions 80° < |β| ≤110° waves are diffracted around the structure and an

adjustment of the wave height Hm0 and the wave period Tm-1,0 are recommended:

Hm0 is multiplied by 30

Tm-1,0 is multiplied by

For wave directions between 110° < |β| ≤180° wave run-up and wave overtopping are set

to Ru2%=0 and q=0.

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Figure 5.24: Influence factor γβ for oblique wave attack and short crested waves, measured data

are for wave run-up

No significant influence of different spreading widths s (s = ∞, 65, 15 and 6) was found in

model tests. As long as some spreading is present, short-crested waves behave similar

independent of the spreading width. The main point is that short-crested oblique waves

give different wave run-up and wave overtopping than long-crested waves.

5.3.4 Composite slopes and berms

(a) Average slopes: Many dikes do not have a straight slope from the toe to the

crest but consist of a composite profile with different slopes, a berm or multiple berms. A

characteristic slope is required to be used in the breaker parameter ξm-1,0 for composite

profiles or bermed profiles to calculate wave run-up or wave overtopping. Theoretically,

the run-up process is influenced by a change of slope from the breaking point to the

maximum wave run-up height. Therefore, often it has been recommended to calculate the

characteristic slope from the point of wave breaking to the maximum wave run-up height.

This approach needs some calculation effort, because of the iterative solution since the

wave run-up height Ru2% is unknown. For the breaking limit a point on the slope can be

chosen which is 1.5 Hm0 below the still water line.

It is recommended to use also a point on the slope 1.5 Hm0 above water as a first estimate

to calculate the characteristic slope and to exclude a berm (Figure 5.25).

1st estimate: BL

Slope

m

tanα 5.25

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Figure 5.25: Determination of the average slope (1st estimate)

As a second estimate , the wave run-up height from the first estimate is used to calculate

the average slope (LSlope has to be adapted see Figure 5.26):

2nd estimate:

Slope

estimatestfromum

tanα 5.26

If the run-up height or 1.5 Hm0 comes above the crest level, then the crest level must be

taken as the characteristic point above SWL.

Figure 5.26: Determination of the average slope (2nd estimate)

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(b) Influence of Berms: A berm is a part of a dike profile in which the slope varies

between horizontal and 1:15 (see Section 1.4 for a detailed definition). A berm is defined

by the width of the berm B and by the vertical difference dB between the middle of the

berm and the still water level (Figure 5.27). The width of the berm B may not be greater

than 0.25⋅L0. If the berm is horizontal, the berm width B is calculated according to

Figure 5.27. The lower and the upper slope are extended to draw a horizontal berm

without changing the berm height dB. The horizontal berm width is therefore shorter than

the angled berm width. dB is zero if the berm lies on the still water line. The characteristic

parameters of a berm are defined in Figure 5.27.

Figure 5.27: Determination of the characteristic berm length LBerm

Figure 5.28: Typical berms (photo: Schüttrumpf)

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A berm reduces wave run-up or wave overtopping. The influence factor γb for a berm

consists of two parts.

( ) 0.16.0 :for 11 ≤≤−−= bdbBb rr γγ 5.27

The first part (rB) stands for the width of the berm LBerm and becomes zero if no berm is

present.

Berm

Br = 5.28

The second part (rdb) stands for the vertical difference dB between the still water level

(SWL) and the middle of the berm and becomes zero if the berm lies on the still water line.

The reduction of wave run-up or wave overtopping is maximum for a berm on the still

water line and decreases with increasing dB. Thus, a berm lying on the still water line is

most effective. A berm lying below 2·Hm0 or above Ru2% has no influence on wave run-up

and wave overtopping.

Different expressions are used for rdB in Europe. Here an expression using a

cosine-function for rdb (Figure 5.29) is recommended which is also used in

PC-Overtopping.

cos5.05.0

u b db R

d r π for a berm above still water line

cos5.05.0

m b db H

dr π for a berm below still water line

rdb=1 for berms lying outside the area of influence

The maximum influence of a berm is actually always limited to γB = 0.6. This corresponds

to an optimal berm width B on the still water line of B = 0.4·Lberm.

The definition of a berm is made for a slope smoother than 1:15 while the definition of a

slope is made for slopes steeper than 1:8, see Section 1.4. If a slope or a part of the

slope lies in between 1:8 and 1:15 it is required to interpolate between a bermed profile

and a straight profile. For wave run-up this interpolation is written by:

tan8/1

−⋅−+= αslopeuBermuslopeuu RRRR 5.30

A similar interpolation procedure should be followed for wave overtopping.

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Figure 5.29: Influence of the berm depth on factor rdh

5.3.5 Effect of wave walls

In some cases a vertical or very steep wall is placed on the top of a slope to reduce wave

overtopping. Vertical walls on top of the slope are often adopted if the available place for

an extension of the basis of the structure is restricted. These are essentially relatively

small walls and not large vertical structures such as caissons and quays (these are

treated separately in Chapter 7). The wall must form an essential part of the slope, and

sometimes includes a berm or part of the crest. The effectiveness of a wave wall to

reduce wave run-up and wave overtopping might be significant (Figure 5.31).

Figure 5.30: Sea dike with vertical crest wall (photo: Hofstede)

The knowledge about the influence of vertical or steep walls on wave overtopping is quite

limited and only a few model studies are available. Based on this limited information, the

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influence factors for a vertical or steep wall apply for the following studied application

area:

• the average slope of 1.5 Hm0 below the still water line to the foot of the wall

(excluding a berm) must lie between 1:2.5 to 1:3.5.

• the width of all berms together must be no more than 3 Hm0.

• the foot of the wall must lie between about 1.2 Hm0 under and above the still water

line;

• the minimum height of the wall (for a high foot) is about 0.5 Hm0. The maximum

height (for a low foot) is about 3 Hm0.

Figure 5.31: Influence of a wave wall on wave overtopping (photo: Schüttrumpf)

It is possible that work will be performed to prepare guidance for wave overtopping for

vertical constructions on a dike or embankment, in the future. Until then the influence

factors below can be used within the application area described. Wave overtopping for a

completely vertical walls is given in Chapter 7 of this manual.

For wave overtopping a breaker parameter is required, as for wave run-up. A vertical wall

soon leads to a large value for the breaker parameter when determining an average slope

as described in Figure 5.25. This means that the waves will not break. The wall will be on

top of the slope, possibly even above the still water line, and the waves will break on the

slope before the wall. In order to maintain a relationship between the breaker parameter

and the type of breaking on the dike slope, the steep or vertical wall must be drawn as a

slope 1:1 when determining the average slope. This slope starts at the foot of the vertical

wall. The average slope and the influence of any berm must be determined with a 1:1

slope instead of the actual steep slope or vertical wall, according to the procedure given

before.

Furthermore, the overtopping for a vertical wall on the top of a dike is smaller than for a

1:1 slope on top of a dike profile. The influence factor for a vertical wall on a slope is

γV = 0.65. For a 1:1 slope, this influence factor is γV = 1. Interpolation must be performed

for a wall that is steeper than 1:1 but not vertical:

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wallv αγ ⋅−= 0078.035.1 5.31

where αwall is the angle of the steep slope in degrees (between 45º for a 1:1 slope and 90º

for a vertical wall).

The method to calculate the reduction factor for vertical walls is very limited to the given

conditions. Therefore, it is recommended to use the Neural Network for more reliable

calculations.

5.4 Overtopping volumes

An average overtopping discharge does not say much about the load of the dike or

revetment caused by individual waves. The significance of the individual overtopping

volumes can be shown from the example in Figure 5.32, which gives the probability

distribution function of individual overtopping volumes for an average overtopping

discharge of 1.7 l/s per m, a wave period of Tm-1,0=5 s and for 7% of overtopping waves.

In this Figure 50 % of the overtopping waves result in an overtopping volume of less than

0.06 m3 per m width but 1 % of the overtopping waves result in an overtopping volume of

more than 0.77 m3 per m width, which is more than 10 times larger.

The overtopping volumes per wave can be described by a Weibull distribution with a

shape factor of 0.75 and a scale factor a. It is a sharply upward bound curve in

Figure 5.32, showing that only a few very large overtopping waves count for most of the

overtopping discharge. The shape factor was found to be almost constant. The scale

factor a depends on the average overtopping rate q, the mean wave period Tm and the

probability of overtopping waves Pov. The Weibull distribution giving the exceedance

probability PV of an overtopping volume per wave V is described as:

exp1

a

with:

ov m P

qTa ⋅⋅= 84.0 5.33

If the overtopping volume per wave for a given probability of exceedance PV is required:

( )[ ] 3/41ln VPaV −−⋅= 5.34

For the maximum overtopping volume in a storm the following formula can be used, by

filling in the number of overtopping waves Nov. Note that the prediction of this maximum

volume is subject to quite some uncertainty, which is always the case for a maximum in a

distribution.

( )[ ] 3/4max ln ovNaV ⋅= 5.35

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The probability of overtopping per wave can be calculated by assuming a

Rayleigh-distribution of the wave run-up heights and taking Ru2% as a basis :

02.0lnexp

u

ov R

The probability of overtopping per wave Pov is related to the number of incoming (Nw) and

overtopping waves (Now) by:

w ow ov N

Example:

The probability distribution function for wave overtopping volumes per wave is calculated

for a smooth tanα = 1:6 dike with a freeboard of RC = 2.0 m, a period of the incoming wave

of Tm-1,0 = 5.0 s and a wave height of the incoming waves of Hm0 = 2.0 m. For these

conditions, the wave run-up height is Ru2% = 2.43 m, the average overtopping rate

q = 1.7 l/(sm) and the probability of overtopping per wave is Pov = 0.071. This means, that

the scale factor a becomes a = 0.100. The storm duration is assumed to be 1 hour,

resulting in 720 incoming waves and 51 overtopping waves. The probability of

exceedance curve is given in Figure 5.32.

Figure 5.32: Example probability distribution for wave overtopping volumes per wave

5.5 Overtopping flow velocities and overtopping flow depth

Average overtopping rates are not appropriate to describe the interaction between the

overtopping flow and the failure mechanisms (infiltration and erosion) of a clay dike.

Therefore, research was carried out recently in small and large scale model tests to

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investigate the overtopping flow (see Figure 5.33) velocities and the related flow depth on

the seaward slope, the dike crest and the landward slope. Results are summarized in

Schüttrumpf and Van Gent, 2003. Empirical and theoretical functions were derived and

verified by experimental data in small and large scale. These parameters are required as

boundary conditions for geotechnical investigations, such as required for the analysis of

erosion, infiltration and sliding.

The parameters for overtopping flow velocities and overtopping flow depth will be

described separately for the seaward slope, the dike crest and the landward slope.

Figure 5.33: Wave overtopping on the landward side of a seadike (photo: Zitscher)

5.5.1 Seaward Slope

Wave run-up velocities and related flow depths are required on the seaward slope to

determine the initial flow conditions of wave overtopping at the beginning of the dike crest.

(a) Wave run-up flow depth: The flow depth of wave run-up on the seaward slope is

a function of the horizontal projection xZ of the wave run-up height Ru2%, the position on

the dike xA and a dimensionless coefficient c2. The flow depth of wave run-up on the

seaward slope can be calculated by assuming a linear decrease of the layer thickness hA

from SWL to the highest point of wave run-up:

( ) ( ) *22* xcxxcxh AzA ⋅=−= 5.38

with x* the remaining run-up length (x* = xZ - xA) and xz = Ru2%/tanα.

No distinction is required here for non-breaking and breaking waves since wave breaking

is considered in the calculation of the wave run-up height Ru2%. The coefficient c2 can be

determined for different exceedance levels by Table 5.3.

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Table 5.3: Characteristic values for parameter c2 (TMA-spectra)

Parameter c2 σ’

Figure 5.34: Definition sketch for layer thickness and wave run-up velocities on the seaward slope

(b) Wave Run-up Velocities: The wave run-up velocity is defined as the maximum

velocity that occurs during wave run-up at any position on the seaward slope. This

velocity is attributed to the front velocity of the wave run-up tongue. The wave run-up

velocity can be derived from a simplified energy equation and is given by:

( )AuA zRgkv −⋅= %2* 2 5.39

with vA the wave run-up velocity at a point zA above SWL, Ru2% the wave run-up height

exceeded by 2% of the incoming waves, and k* a dimensionless coefficient.

In dimensionless form, the wave run-up velocity is:

Ra gH )z(v Au2%*

Equation 5.40 has been calibrated by small and large scale model data resulting in values

for the 2%, 10% and 50% exceedance probability (Table 5.4).

Exemplarily, the decrease of wave run-up velocity and wave run-up flow depth on the

seaward slope is given in Figure 5.35.

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Table 5.4: Characteristic Values for Parameter a0* (TMA-spectra)

Parameter a0* σ’

Figure 5.35: Wave run-up velocity and wave run-up flow depth on the seaward slope (example)

5.5.2 Dike Crest

The overtopping tongue arrives as a very turbulent flow at the dike crest (Figure 5.36).

The water is full of air bubbles and the flow can be called “white water flow”. Maximum

flow depth and overtopping velocities were measured in this overtopping phase over the

crest. The overtopping flow separates slightly from the dike surface at the front edge of

the crest. No flow separation occurs at the middle and at the rear edge of the crest. In

the second overtopping phase, the overtopping flow has crossed the crest. Less air is in

the overtopping flow but the flow itself is still very turbulent with waves in flow direction

and normal to flow direction. In the third overtopping phase, a second peak arrives at the

crest resulting in nearly the same flow depth as the first peak. In the fourth overtopping

phase, the air has disappeared from the overtopping flow and both overtopping velocity

and flow depth are decreasing. Finally, the overtopping flow nearly stops on the dike crest

for small overtopping flow depths. Few air is in the overtopping water. At the end of this

phase, the overtopping water on the dike crest starts flowing seaward.

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Test conditions:

Regular wave: H=1.0m; T=9.5s; h=5.0m

Dike geometry: RC=1.0m; 1:n = 1:6; 1:m = 1:3; BC=2.0m

Average overtopping discharge: q=120 l/(sm)

Figure 5.36: Sequence showing the transition of overtopping flow on a dike crest (Large Wave

Flume, Hannover)

The flow parameters at the transition line between seaward slope and dike crest are the

initial conditions for the overtopping flow on the dike crest. The evolution of the

overtopping flow parameters on the dike crest will be described below.

(a) Overtopping flow depth on the dike crest: The overtopping flow depth on the

dike crest depends on the width of the crest B and the co-ordinate on the crest xC

(Figure 5.37). The overtopping flow depth on the dike crest decreases due to the fact that

the overtopping water is deformed. Thus, the decrease of overtopping flow depth over the

dike crest can be described by an exponential function:

x exp

0)(xh

)(xh

c xc xc

with hC the overtopping flow depth on the dike crest, xC the horizontal coordinate on the

dike crest with xC = 0 at the beginning of the dike crest, c3 the dimensional coefficient

= 0.89 for TMA spectra (σ’=0.06) and 1.11 for natural wave spectra (σ’=0.09), and BC the

width of the dike crest (for Bc = 2 to 3 m in prototype scale).

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Figure 5.37: Definition sketch for overtopping flow parameters on the dike crest

(b) Overtopping flow velocity: A theoretical function for overtopping flow velocities

on the dike crest has been developed by using the simplified Navier-Stokes-equations and

the following assumptions: the dike crest is horizontal; velocities vertical to the dike slope

can be neglected; the pressure term is almost constant over the dike crest; viscous effects

in flow direction are small; bottom friction is constant over the dike crest

The following formula was derived from the Navier-Stokes-equations and verified by small

and large scale model tests (Figure 5.38):

xCC h

fx vv

exp)0( 5.42

with vC the overtopping flow velocity on the dike crest; vC,(Xc=0) the overtopping flow velocity

at the beginning of the dike crest (xC=0); xC the coordinate along the dike crest; f the

friction coefficient; and hC the flow depth at xC.

From Equation 5.43 it is obvious that the overtopping flow velocity on the dike crest is

mainly influenced by bottom friction. The overtopping flow velocity decreases from the

beginning of the dike crest to the end of the dike crest due to bottom friction. The friction

factor f was determined from model tests at straight and smooth slope to be f=0.01. The

importance of the friction factor on the overtopping flow velocities on the dike crest is

obvious from Figure 5.39. The overtopping flow velocity decreases significantly over the

dike crest for increasing surface roughness. But for flow depths larger than about 0.1 m

and dike crest widths around 2 – 3 m, the flow depth and velocity hardly change over the

crest.

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Figure 5.38: Overtopping flow velocity data compared to the overtopping flow velocity formula

Figure 5.39: Sensitivity analysis for the dike crest (left side: influence of overtopping flow depth on

overtopping flow velocity; right side: influence of bottom friction on overtopping flow

velocity)

5.5.3 Landward Slope

The overtopping water flows from the dike crest to the landward slope of the dike. The

description of the overtopping process on the landward slope is very important with

respect to dike failures which often occurred on the landward slope in the past. An

analytical function was developed which describes overtopping flow velocities and

overtopping flow depths on the landward slope as a function of the overtopping flow

velocity at the end of the dike crest (vb,0 = vC(xC=B)), the slope angle β of the landward

side and the position sB on the landward side with sB=0 at the intersection between dike

crest and landward slope. A definition sketch is given in Figure 5.41. The following

assumptions were made to derive an analytical function from the Navier-StokesEurOtop Manual

equations: velocities vertical to the dike slope can be neglected; the pressure term is

almost constant over the dike crest; and the viscous effects in flow direction are small.

Figure 5.40: Overtopping flow on the landward slope (Large Wave Flume, Hannover) (photo:

Schüttrumpf)

This results in the following formula for overtopping flow velocities:

tk tanh

k h

vf

tk tanh

f hkv

v

1b b,0

1b1

b,0

b with:

βββ sin g

s 2

sin g

v sin g

v - t b22

bb,0 ++≈ and

b 1 h

sinβ g f 2k =

Equation 5.44 needs an iterative solution since the overtopping flow depth hb and the

overtopping flow velocity vb on the landward slope are unknown. The overtopping flow

depth hb can be replaced in a first step by:

b b,0b,0

b v

hv h

with vb,0 the overtopping flow velocity at the beginning of the landward slope

(vb,0=vB(sB=0)); and hb,0 the overtopping flow depth at the beginning of the landward slope

(hb,0 =hB (sB =0)).

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Figure 5.41: Definition of overtopping flow parameters on the landward slope

In Figure 5.42, the influence of the landward slope on overtopping flow velocities and

overtopping flow depths is shown. The landward slope was varied between 1:m = 1:2 and

1:m = 1:6 which is in the practical range. It is obvious that overtopping flow velocities

increase for steeper slopes and related overtopping flow depths decrease with increasing

slope steepness.

Figure 5.42: Sensitivity Analysis for Overtopping flow velocities and related overtopping flow depths

– Influence of the landward slope The second important factor influencing the overtopping flow on the landward slope is the

bottom friction coefficient f which has to be determined experimentally. Some references

for the friction coefficient on wave run-up are given in literature (e.g. Van Gent, 1995;

Cornett and Mansard, 1994, Schulz, 1992). Here, the bottom friction coefficient was

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determined by comparison of the experimental to be f = 0.02 for a smooth and straight

slope. These values are comparable to references in literature. Van Gent (1995)

recommends a friction coefficient f = 0.02 for smooth slopes and Schulz (1992)

determined friction coefficients between 0.017 and 0.022.

The overtopping flow on the landward slope tends towards an asymptote for sb → ∞ which

is given by:

f hg b βsin2 vb

5.6 Scale effects for dikes

A couple of investigations on the influence of wind and scale effects are available for

sloping structures all of which are valid only for rough structures. Sea dikes are generally

smooth and covered e.g. by grass, revetment stones or asphalt which all have roughness

coefficients larger than γf = 0.9. Hence, there are no significant scale effects for these

roughness coefficients. This is however only true if the model requirements as given in

Table 4.3 in Section 4.8.3 are respected.

For rough slopes as they e.g. occur for any roughness elements on the seaward slope,

scale effects for low overtopping rates cannot be excluded and therefore, the procedure

as given in Section 6.3.6 should be applied.

5.7 Uncertainties

In section 5.3.1 model uncertainties have been introduced in the calculation by defining

the parameter b in Equation 5.8 as normally distributed parameter with a mean of 4.75

and a standard deviation of σ = 0.5 for breaking waves and b = 0.2 and σ = 0.35 for non

breaking waves. This has also been illustrated by Figure 5.6 and Figure 5.7, respectively,

showing the 90% confidence interval resulting from these considerations.

In using the approach as proposed in section 4.8.1, a model uncertainty of about 60% is

obtained. Note that this approach comprises a model factor for Equation 5.8 in total rather

than the uncertainty of the parameter b only as used in Figure 5.6 and Figure 5.7. The

latter approach comprise various uncertainties from model tests, incl. repeatability of tests,

model effects, uncertainties in wave measurements, etc. whereas the following

uncertainties for the assessment of the wave heights, the wave period, the water depth,

the wave attack angle, constructional parameters such as the crest height and the slope

angle are not included.

The uncertainties of these parameters may be estimated following an analysis of expert

opinions from Schüttrumpf et al. (2006) using coefficients of variations (CoV) for the wave

height Hm0 (3.6%), the wave period (4.0%), and the slope angle (2.0%). Other parameters

are independent of their mean values so that standard deviations can be used for the

water depth (0.1 m), the crest height and the height of the berm (0.06 m), and the friction

factor (0.05). It should be noted that these uncertainties should only be used if no better

information (e.g. measurements of waves) are obtainable.

Using these values together with the already proposed model uncertainties for the

parameter b in Equation 5.8, crude Monte Carlo simulations were performed to obtain the

uncertainty in the resulting mean overtopping discharges. Plots of these results are shown

in Figure 5.43.

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dimensionless freeboard R* =

di m en si on le ss o ve rto

pp in g ra te

Data points

Std.-dev. (-)

Std.-dev. (+)

n * Std.-dev. (+)

n * Std.-dev. (-)

vfb

m m

tan

Eq. 5.8

Eq. 5.9

Figure 5.43: Wave overtopping over sea dikes, including results from uncertainty calculations

As compared to Figure 5.6 and Figure 5.7, respectively, it can be seen that the resulting

curves (denominated as ‘n*std.-dev.’ in Figure 5.43) are only giving slightly larger

uncertainty bands as the 5% lines resulting from calculations with model uncertainties.

This suggests a very large influence of the model uncertainties so that no other

uncertainties, if assumed to be in the range as given above, need to be considered. It is

therefore proposed to use Equations 5.8 and 5.9 as suggested in section 5.3.1. In case of

deterministic calculations, Equation 5.9 should be used with no further adaptation of

parameters. In case of probabilistic calculations, Equation 5.8 should be used and

uncertainties of all input parameters should be considered in addition to the model

uncertainties. If detailed information of some of these parameters is not available, the

uncertainties as proposed above may be used.

It should be noted that only uncertainties for mean wave overtopping rates are considered

here. Other methods such as flow velocities and flow depths were not considered here but

can be dealt with using the principal procedure as discussed in section 1.5.4.

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6.1 Introduction

This manual describes three types of flood defences or coastal structures:

• coastal dikes and embankment seawalls,

• armoured rubble slopes and structures,

• and vertical and steep seawalls.

Sometimes there will be combinations and it will be difficult to place them only in one

category. For example, a vertical wall or sloping embankment with a large rock berm in

front. Armoured rubble slopes and mounds () are characterized by a mound with some

porosity or permeability, covered by a sloping porous armour layer consisting of large rock

or concrete units. In contrast to dikes and embankment seawalls the porosity of the

structure and armour layer plays a role in wave run-up and overtopping. The

cross-section of a rubble mound slope, however, may have great similarities with an

embankment seawall and may consist of various slopes.

As rubble mound structures are to some extent similar to dikes and embankment

seawalls, the basic wave run-up and overtopping formulae are taken from Chapter 5.

They will then be modified, if necessary, to fit for rubble mound structures. Also for most

definitions the reader is referred to Chapter 5 (or Chapter 1.4). More in particular:

• the definition of wave run-up (Figure 5.3)

• the general wave run-up formula (Equation 5.1)

• the general wave overtopping formula (Equation 5.8 or 5.9)

• the influence factors γb, γf and γβ

• the spectral wave period Tm-1,0

• the difference in deterministic and probabilistic approach

The main calculation procedure for armoured rubble slopes and mounds is given in

Table 6.1.

Table 6.1: Main calculation procedure for armoured rubble slopes and mounds

Deterministic design Probabilistic design

Wave run-up height (2%) Eq. 6.2 Eq. 6.1

Wave runu-up height for shingle beaches Eq. 6.20

Mean wave overtopping discharge Eq. 6.5 Eq. 6.6

Mean overtopping discharge

for berm breakwaters Eq. 6.9 – 6.11

Percentage of overtopping waves Eq. 6.4

Individual overtopping volumes Eqs. 6.15-6.16 Eqs. 6.15-6.16

Effect of armour roughness Table 6.2 Table 6.2

Effect of armour crest berm Eq. 6.7 Eq. 6.7

Effect of oblique waves Eq. 6.8 for overtopping Eq. 6.8 for overtopping

Overtopping velocities Eqs. 6.17 – 6.18

Scale and model uncertenties Eqs. 6.12 – 6.14 Eqs. 6.12 – 6.14

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Figure 6.1 Armoured structures

6.2 Wave run-up and run-down levels, number of overtopping waves

Through civil engineering history the wave run-up and particularly the 2% run-up height

was important for the design of dikes and coastal embankments. Till quite recently the

2% run-up height under design conditions was considered a good measure for the

required dike height. With only 2% of overtopping waves the load on crest and inner side

were considered so small that no special measurements had to be taken with respect to

strength of these parts of a dike. Recently, the requirements for dikes changed to

allowable wave overtopping, making the 2% run-up value less important in engineering

practice.

Wave run-up has always been less important for rock slopes and rubble mound structures

and the crest height of these type of structures has mostly been based on allowable

overtopping, or even on allowable transmission (low-crested structures). Still an

estimation or prediction of wave run-up is valuable as it gives a prediction of the number

or percentage of waves which will reach the crest of the structure and eventually give

wave overtopping. And this number is needed for a good prediction of individual

overtopping volumes per wave.

Figure 6.2 gives 2% wave run-up heights for various rocks slopes with cotα = 1.5, 2, 3 and

4 and for an impermeable and permeable core of the rubble mound. These run-up

measurements were performed during the stability tests on rock slopes of Van der Meer

(1988). First of all the graph gives values for a large range of the breaker parameter ξm-1,0,

due to the fact that various slope angels were tested, but also with long wave periods

(giving large ξm-1,0-values). Most breakwaters have steep slopes 1:1.5 or 1:2 only and

then the range of breaker parameters is often limited to ξm-1,0 = 2-4. The graph gives rock

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slope information outside this range, which may be useful also for slopes with concrete

armour units.

The highest curve in Figure 6.2 gives the prediction for smooth straight slopes, see

Figure 5.1 and Equation 5.3. A rubble mound slope dissipates significantly more wave

energy than an equivalent smooth and impermeable slope. Both the roughness and

porosity of the armour layer cause this effect, but also the permeability of the under layer

and core contribute to it. Figure 6.2 shows the data for an impermeable core (geotextile

on sand or clay underneath a thin under layer) and for a permeable core (such as most

breakwaters). The difference is most significant for large breaker parameters.

Equation 5.1 includes the influence factor for roughness γf. For two layers of rock on an

impermeable core γf = 0.55. This reduces to γf = 0.40 for two layers of rock on a

permeable core. This influence factor is used in the linear part of the run-up formula, say

for ξ0 ≤ 1.8. From ξm-1,0 = 1.8 the roughness factor increases linearly up to 1 for ξm-1,0 = 10

and it remains 1 for larger values. For a permeable core, however, a maximum is reached

for Ru2%/Hm0 = 1.97. The physical explanation for this is that if the slope becomes very

steep (large ξ0-value) and the core is impermeable, the surging waves slowly run up and

down the slope and all the water stays in the armour layer, leading to fairly high run-up.

The surging wave actually does not “feel” the roughness anymore and acts as a wave on

a very steep smooth slope. For an permeable core, however, the water can penetrate into

the core which decreases the actual run-up to a constant maximum (the horizontal line in

Figure 6.2).

Spectral breaker parameter ξm-1,0

u2

m

imp. cota=2 perm. cota=1.5

imp. cota=3 perm. cota=2

imp. cota=4 perm. cota=3

Figure 6.2: Relative run-up on straight rock slopes with permeable and impermeable core,

compared to smooth impermeable slopes

The prediction for the 2% mean wave run-up value for rock or rough slopes can be

described by:

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m u

R ξγγγ β with a maximum of

m surgingfb

m u

From ξm-1,0 = 1.8 the roughness factor γf surging increases linearly up to 1 for

ξm-1,0 = 10, which can be described by:

γf surging = γf + (ξm-1,0 - 1.8)*(1 - γf)/8.2

γf surging = 1.0 for ξm-1,0 > 10.

For a permeable core a maximum is reached for Ru2%/Hm0 = 1.97

Equation 6.1 may also give a good prediction for run-up on slopes armoured with concrete

armour units, if the right roughness factor is applied (see Section 6.3).

Deterministic design or safety assessment: For design or a safety assessment of the

crest height, it is advised not to follow the average trend, but to include the uncertainty of

the prediction, see Section 5.2. As the basic equation is similar for a smooth and a rough

slope, the method to include uncertainty is also the same. This means that for a

deterministic design or safety assessment Equation 5.4 should be used and adapted

accordingly as in Equation 6.1:

m u

R ξγγγ β with a maximum of

m surgingfb

m u

From ξm-1,0 = 1.8 the roughness factor γf surging increases linearly up to 1 for

ξm-1,0 = 10, which can be described by:

γf surging = γf + (ξm-1,0 - 1.8)*(1 - γf)/8.2

γf surging = 1.0 for ξm-1,0 > 10.

For a permeable core a maximum is reached for Ru2%/Hm0 = 2.11

Probabilistic design: For probabilistic calculations Equation 6.1 is used together with a

normal distribution and variation coefficient of σ’ = 0.07. For prediction or comparison of

measurements the same Equation 6.1 is used, but now for instance with the 5% lower and

upper exceedance lines.

Till now only the 2% run-up value has been described. It might be that one is interested in

an other percentage, for example for design of breakwaters where the crest height may be

determined by an allowable percentage of overtopping waves, say 10-15%. A few ways

exist to calculate run-up heights for other percentages, or to calculate the number of

overtopping waves for a given crest height. Van der Meer and Stam (1992) give two

methods. One is an equation like 6.1 with a table of coefficients for the 0.1%, 1%, 2%,

5%, 10% and 50% (median). Interpolation is needed for other percentages.

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The second method gives a formula for the run-up distribution as a function of wave

conditions, slope angle and permeability of the structure. The distribution is a

two-parameter Weibull distribution. With this method the run-up can be calculated for

every percentage wanted. Both methods apply to straight rock slopes only and will not be

described here. The given references, however, give all details.

The easiest way to calculate run-up (or overtopping percentage) different from 2% is to

take the 2%-value and assume a Rayleigh distribution. This is similar to the method in

Chapter 5 for dikes and embankment seawalls. The probability of overtopping

Pov = Now/Nw (the percentage is simply 100 times larger) can be calculated by:

02.0lnexp/

u

wowov R

Equation 6.3 can be used to calculate the probability of overtopping, given a crest

freeboard Rc or to calculate the required crest freeboard, given an allowable probability or

percentage of overtopping waves.

One warning should be given in applying Equations 6.1, 6.2 and 6.3. The equations give

the run-up level in percentage or height on a straight (rock) slope. This is not the same as

the number of overtopping waves or overtopping percentage. Figure 6.3 gives the

difference. The run-up is always a point on a straight slope, where for a rock slope or

armoured mound the overtopping is measured some distance away from the seaward

slope and on the crest, often behind a crown wall. This means that Equations 6.1, 6.2 and

6.3 always give an over estimation of the number of overtopping waves.

1.5 Hm0toe

1.5 Hm0toe

swl

overtopping

measured

behind wall

RcAc

Gc run-up level (eq. 6.1 and

6.2) calculated here

Figure 6.3: Run-up level and location for overtopping differ

Figure 6.4 shows measured data for rubble mound breakwaters armoured with Tetrapods

(De Jong 1996), Accropode™ or a single layer of cubes (Van Gent et al. 1999). All tests

were performed at Delft Hydraulics. The test set-up was more or less similar to Figure 6.2

with a crown wall height Rc a little lower than the armour freeboard Ac. CLASH-data on

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specific overtopping tests (see Section 6.3) for various rock and concrete armoured

slopes were added to Figure 6.4. This figure gives only the percentage of overtopping

waves passing the crown wall. Analysis showed that the size of the armour unit relative to

the wave height had influence, which gave a combined parameter Ac*Dn/Hm02, where Dn is

the nominal diameter of the armour unit.

The figure covers the whole range of overtopping percentages, from complete overtopping

with the crest at or lower than SWL to no overtopping at all. The CLASH data give

maximum overtopping percentages of about 30%. Larger percentages mean that

overtopping is so large that it can hardly be measured and that wave transmission starts

to play a role.

Taking 100% overtopping for zero freeboard (the actual data are only a little lower), a

Weibull curve can be fitted through the data. Equation 6.4 can be used to predict the

number or percentage of overtopping waves or to establish the armour crest level for an

allowable percentage of overtopping waves.

exp/

m nc wowov H

It is clear that equations 6.1 - 6.3 will come to more overtopping waves than equation 6.4.

But both estimations together give a designer enough information to establish the required

crest height of a structure given an allowable overtopping percentage.

Dimensionless crest height Ac*Dn/Hm02

Pe rc en ta ge o f o

ve rto

pp in g w av es

Tetrapod DH

Accropode(TM) DH

1 layer cube DH

Figure 6.4: Percentage of overtopping waves for rubble mound breakwaters as a function of

relative (armour) crest height and armour size (Rc ≤ Ac)

When a wave on a structure has reached its highest point it will run down on the slope till

the next wave meets this water and run-up starts again. The lowest point to where the

water retreats, measured vertically to SWL, is called the run-down level. Run-down often

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is less or not important compared to wave run-up, but both together they may give an idea

of the total water excursion on the slope. Therefore, only a first estimate of run-down on

straight rock slopes is given here, based on the same tests of Van der Meer (1988), but

re-analysed with respect to the use of the spectral wave period Tm-1,0. Figure 6.5 gives an

overall view.

The graph shows clearly the influence of the permeability of the structure as the solid data

points (impermeable core) generally show larger run-down than the open data symbols of

the permeable core. Furthermore, the breaker parameter ξm-1,0 gives a fairly clear trend of

run-down for various slope angles and wave periods. Figure 6.5 can be used directly for

design purposes, as it also gives a good idea of the scatter.

Breaker parameter ξm-1,0

el at iv e ru ndo w n

d2

m

imp; cota=2 imp; cota=3

imp; cota=4 perm; cota=1.5

perm; cota=2 perm; cota=3

hom; cota=2 imp; Deltaflume

perm; Deltaflume

Figure 6.5: Relative 2% run-down on straight rock slopes with impermeable core (imp), permeable

core (perm) and homogeneous structure (hom)

6.3 Overtopping discharges

6.3.1 Simple armoured slopes

The mean overtopping discharge is often used to judge allowable overtopping. It is easy

to measure and an extensive database on mean overtopping discharge has been

gathered in CLASH. This mean discharge does of course not describe the real behaviour

of wave overtopping, where only large waves will reach the top of the structure and give

overtopping. Random individual wave overtopping means random in time and each wave

gives a different overtopping volume. But the description of individual overtopping is

based on the mean overtopping, as the duration of overtopping multiplied with this mean

overtopping discharge gives the total volume of water overtopped by a certain number of

overtopping waves. The mean overtopping discharge has been described in this section.

The individual overtopping volumes is the subject in Section 6.4

Just like for run-up, the basic formula for mean wave overtopping discharge has been

described in Chapter 5 for smooth slopes (Equation 5.8 or 5.9). The influence factor for

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roughness should take into account rough structures. Rubble mound structures often

have steep slopes of about 1:1.5, leading to the second part in the overtopping equations.

Deterministic design or safety assessment: The equation, including a standard

deviation of safety, should be used for deterministic design or safety assessment:

m

Hg q

3.2exp2.0 6.5

Probabilistic design: The mean prediction should be used for probabilistic design, or

prediction of or comparison with measurements. This equation is given by:

m

Hg q

6.2exp2.0 6.6

The coefficient 2.6 in Equation 6.6 gives the mean prediction and its reliability can be

described by a standard deviation of σ = 0.35.

As part of the EU research programme CLASH (Bruce et al. 2007) tests were undertaken

to derive roughness factors for rock slopes and different armour units on sloping

permeable structures. Overtopping was measured for a 1:1.5 sloping permeable structure

at a reference point 3Dn from the crest edge, where Dn is the nominal diameter. The wave

wall had the same height as the armour crest, so Rc = Ac. As discussed in Section 6.2

and Figure 6.3, the point to where run-up can be measured and the location of

overtopping may differ. Normally, a rubble mound structure has a crest width of at least

3Dn. Waves rushing up the slope reach the crest with an upward velocity. For this reason

it is assumed that overtopping waves reaching the crest, will also reach the location 3Dn

further.

Results of the CLASH-work is shown in Figure 6.6 and Table 6.2. Figure 6.6 gives all

data together in one graph. Two lines are given, one for a smooth slope, Equation 6.4

with γf = 1.0, and one for rubble mound 1:1.5 slopes, with the same equation, but with

γf = 0.45. The lower line only gives a kind of average, but shows clearly the very large

influence of roughness and permeability on wave overtopping. The required crest height

for a steep rubble mound structure is at least half of that for a steep smooth structure, for

similar overtopping discharge. It is also for this reason that smooth slopes are often more

gentle in order to reduce the crest heights.

In Figure 6.6 one-layer systems, like Accropode™, CORE-LOC®, Xbloc® and 1 layer of

cubes, have solid symbols. Two-layer systems have been given by open symbols. There

is a slight tendency that one-layer systems give a little more overtopping than two-layer

systems, which is also clear from Table 6.2. Equation 6.4 can be used with the roughness

factors in Table 6.2 for prediction of mean overtopping discharges for rubble mound

breakwaters. Values in italics in Table 6.2 have been estimated / extrapolated, based on

the CLASH results.

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Relative crest height Rc/Hm0

av e ov er to pp in g q/ (g

m

Smooth Rock Cube rough

Cube flat Anitfer Haro

Tetrapod Cube-1 layer Accropde™

Coreloc™ Xbloc smooth gf=1.0

rough gf=0.45

Figure 6.6: Mean overtopping discharge for 1:1.5 smooth and rubble mound slopes

Table 6.2: Values for roughness factor γf for permeable rubble mound structures with slope of

1:1.5. Values in italics are estimated/extrapolated

Type of armour layer γf

Smooth impermeable surface 1.00

Rocks (1 layer, impermeable core) 0.60

Rocks (1 layer, permeable core) 0.45

Rocks (2 layers, impermeable core) 0.55

Rocks (2 layers, permeable core) 0.40

Cubes (1 layer, random positioning) 0.50

Cubes (2 layers, random positioning) 0.47

Antifers 0.47

Accropode™, , 0.46

Xbloc® 0.45

Tetrapods 0.38

Dolosse 0.43

6.3.2 Effect of armoured crest berm

Simple straight slopes including an armoured crest berm of less than about 3 nominal

diameters (Gc ≈ 3Dn) will reduce overtopping. It is, however, possible to reduce

overtopping with a wide crest as much more energy can be dissipated in a wider crest.

Besley (1999) describes in a simple and effective way the influence of a wide crest. First

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the wave overtopping discharge should be calculated for a simple slope, with a crest width

up to 3Dn. Then the following reduction factor on the overtopping discharge can be

applied:

( )05.1exp06.3 mcr HGC −= 0mc HG with maximum 1=rC 6.7

Equation 6.7 gives no reduction for a crest width smaller than about 0.75 Hm0. This is

fairly close to about 3Dn and is, therefore, consistent. A crest width of 1 Hm0 reduces the

overtopping discharge to 68%, a crest width of 2 Hm0 gives a reduction to 15% and for a

wide crest of 3 Hm0 the overtopping reduces to only 3.4%. In all cases the crest wall has

the same height as the armour crest: Rc = Ac.

Equation 6.7 was determined for a rock slope and can be considered as conservative, as

for a slope with Accropode more reduction was found.

6.3.3 Effect of oblique waves

Section 5.5.3 describes the effect of oblique waves on run-up and overtopping on smooth

slopes (including some roughness). But specific tests on rubble mound slopes were not

performed at that time. In CLASH, however, this omission was discovered and specific

tests on a rubble mound breakwater were performed with a slope of 1:2 and armoured

with rock or cubes (Andersen and Burcharth, 2004). The structure was tested both with

long-crested and short-crested waves, but only the results by short-crested waves will be

given.

For oblique waves the angle of wave attack β (deg.) is defined as the angle between the

direction of propagation of waves and the axis perpendicular to the structure (for

perpendicular wave attack: β = 0˚). And the direction of wave attack is the angle after any

change of direction of the waves on the foreshore due to refraction. Just like for smooth

slopes, the influence of the angle of wave attack is described by the influence factor γβ.

Just as for smooth slopes there is a linear relationship between the influence factor and

the angle of wave attack, but the reduction in overtopping is much faster with increasing

angle:

for |β| > 80˚ the result β = 80˚ can be applied

The wave height and period are linearly reduced to zero for 80˚ ≤ |β| ≤ 110˚, just like for

smooth slopes, see Section 5.3.3. For |β| > 110˚ the wave overtopping is assumed to be

q = 0 m3/s/m.

6.3.4 Composite slopes and berms, including berm breakwaters

In every formula where a cotα or breaker parameter ξm-1,0 is present, a procedure has to

be described how a composite slope has to be taken into account. Hardly any specific

research exists for rubble mound structures and, therefore, the procedure for composite

slopes at sloping impermeable structures like dikes and sloping seawalls is assumed to be

applicable. The procedure has been described in Section 5.3.4.

Also the influence of a berm in a sloping profile has been described in Section 5.3.4 and

can be used for rubble mound structures. There is, however, often a difference in effect of

composite slopes or berms for rubble mound and smooth gentle slopes. On gentle slopes

the breaker parameter ξm-1,0 has large influence on wave overtopping, see Equations 5.8

and 5.9 as the breaker parameter will be quite small. Rubble mound structures often have

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a steep slope, leading to the formula for “non-breaking” waves, Equations 6.5 and 6.6. In

these equations there is no form factor present.

This means that a composite slope and even a, not too long, berm leads to the same

overtopping discharge as for a simple straight rubble mound slope. Only when the

average slope becomes so gentle that the maximum in Equations 5.8 or 5.9 does not

apply anymore, then a berm and a composite slope will have effect on the overtopping

discharge. Generally, average slopes around 1:2 or steeper do not show influence of the

slope angle, or only to a limited extend.

A specific type of rubble mound structure is the berm breakwater (see Figure 6.7). The

original idea behind the berm breakwater is that a large berm, consisting of fairly large

rock, is constructed into the sea with a steep seaward face. The berm height is higher

than the minimum required for construction with land based equipment. Due to the steep

seaward face the first storms will reshape the berm and finally a structure will be present

with a fully reshaped S-profile. Such a profile has then a gentle 1:4 or 1:5 slope just below

the water level and steep upper and lower slopes, see Figure 6.8.

Figure 6.7 Icelandic Berm breakwater

Figure 6.8: Conventional reshaping berm breakwater

The idea of the reshaping berm breakwater has evolved in Iceland to a more or less nonreshaping berm breakwater. The main difference is that during rock production from the

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quarry care is taken to gather a few percent of really big rock. Only a few percent is

required to strengthen the corner of the berm and part of the down slope and upper layer

of the berm in such a way that reshaping will hardly occur. An example with various rock

classes (class I being the largest) is given in Figure 6.9. Therefore distinction has been

made between conventional reshaping berm breakwaters and the non-reshaping Icelandic

type berm breakwater.

Figure 6.9: Non-reshaping Icelandic berm breakwater with various classes of big rock

In order to calculate wave overtopping on reshaped berm breakwaters the reshaped

profile should be known. The basic method of profile reshaping is given in Van der Meer

(1988) and the programme BREAKWAT (WL | Delft Hydraulics) is able to calculate the

profile. The first method described here to calculate wave overtopping at reshaping berm

breakwaters is the method described in Chapter 5 (equations 5.8 or 5.9) with the

roughness factors given in Table 6.1 of γf = 0.40 for reshaping berm breakwaters and

γf = 0.35 for non-reshaping Icelandic berm breakwaters. The method of composite slopes

and berms should be applied as described above.

The second method is to use the CLASH neural network (Section 4.4). As overtopping

research at that time on berm breakwaters was limited, also this method gives quite some

scatter, but a little less than the first method described above.

Recent information on berm breakwaters has been described by Lykke Andersen (2006).

Only part of his research was included in the CLASH database and consequently in the

Neural Network prediction method. He performed about 600 tests on reshaping berm

breakwaters and some 60 on non-reshaping berm breakwaters (fixing the steep slopes by

a steel net). The true non-reshaping Icelandic type of berm breakwaters with large rock

classes, has not been tested and, therefore, his results might lead to an overestimation.

One comment should be made on the application of the results of Lykke Andersen (2006).

The maximum overtopping discharge measured was only q/(gHm03)0.5 = 10-3. In practical

situations with wave heights around 5 m the overtopping discharge will then be limited to

only a few l/s per m width. For berm breakwaters and also for conventional rubble slopes

and mounds allowable overtopping may be much higher than this value.

The final result of the work of Lykke Andersen (2006) is a quite complicated formula,

based on multi-parameter fitting. The advantage of such a fitting is that by using a large

number of parameters, the data set used will be quite well described by the formula. The

disadvantage is that physical understanding of the working of the formula, certainly

outside the ranges tested, is limited. But due to the fact that so many structures were

tested, this effect may be negligible.

The formula is valid for berm breakwaters with no superstructure and gives the

overtopping discharge at the back of the crest (Ac = Rc). In order to overcome the

problem that one has to calculate the reshaped profile before any overtopping calculation

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can be done, the formula is based on the “as built” profile, before reshaping. Instead of

calculating the profile, a part of the formula predicts the influence of waves on recession of

the berm. The parameter used is called fH0, which is an indicative measure of the

reshaping and can be defined as a “factor accounting for the influence of stability

numbers”. Note that fH0 is a dimensionless factor and not the direct measure of recession

and that H0 and T0 are also dimensionless parameters.

( )05.000 08.7exp8.19 Hsf mH −= − for T0 ≥ T0*

5.1005.0 000 += THfH for T0 < T0

where H0 = Hm0/ΔDn50, T0 = (g/Dn50)0.5 Tm0,1,

and T0* = {19.8 s0m-0.5 exp(-7.08/H0) -10.5}/(0.05 H0).

The berm level dh is also taken into account as an influence factor, dh*. Note that the berm

depth is positive if the berm level is below SWL, and therefore, for berm breakwaters often

negative. Note also that this influence factor is different than for a bermed slope, see

Section 5.3.4. This influence factor is described by:

( ) ( )cmhmh RHdHd +−= 00* 3/3 for dh < 3Hm0

0* =hd for dh ≥ 3Hm0

The final overtopping formula then takes into account the influence factor on recession,

fH0, the influence factor of the berm level, dh*, the geometrical parameters Rc, B and Gc,

the wave conditions Hm0 and the mean period Tm0,1. It means that the wave overtopping is

described by a spectral mean period, not by Tm-1,0.

b m c m c

Bh

opH

m esf

gH q

Equation 6.11 is only valid for a lower slope of 1:1.25 and an upper slope of 1:1.25. For

other slopes one has to reshape the slope to a slope of 1:1.25, keeping the volume of

material the same and adjusting the berm width B and for the upper slope also the crest

width Gc. Note also that in Equation 6.11 the peak wave period Tp has to be used to

calculate sop, where the mean period Tm0,1 has to be used in Equation 6.9.

Although no tests were performed on the non-reshaping Icelandic berm breakwaters (see

Figure 6.7), a number of tests were performed on non-reshaping structures by keeping the

material in place with a steel net. The difference may be that Icelandic berm breakwaters

show a little less overtopping, due to the presence of larger rock and, therefore, more

permeability. The tests showed that Equation 6.11 is also valid for non-reshaping berm

breakwaters, if the reshaping factor fH0 = 0.

6.3.5 Effect of wave walls

Most breakwaters have a wave wall, capping wall or crest unit on the crest, simply to end

the armour layer in a good way and to create access to the breakwater. For design it is

advised not to design a wave wall much higher than the armour crest, for the simple

reason that wave forces on the wall will increase drastically if directly attacked by waves

and not hidden behind the armour crest. For rubble mound slopes as a shore protection,

design waves might be a little lower than for breakwaters and a wave wall might be one of

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the solutions to reduce wave overtopping. Nevertheless, one should realise the increase

in wave forces if designing a wave wall significantly above the armour crest.

Equations 6.5 and 6.6 for a simple rubble mound slope includes a berm of 3Dn wide and a

wave wall at the same level as the armour crest: Ac = Rc. A little lower wave wall will

hardly give larger overtopping, but no wave wall at all would certainly increase

overtopping. Part of the overtopping waves will then penetrate through the crest armour.

No formula are present to cope with such a situation, unless the use of the Neural

Network prediction method (Section 4.4).

Various researchers have investigated wave walls higher than the armour crest. None of

them compared their results with a graph like Figure 6.6 for simple rubble mound slopes.

During the writing of this manual some of the published equations were plotted in Figure

6.6 and most curves fell within the scatter of the data. Data with a wider crest gave

significantly lower overtopping, but that was due to the wider crest, not the higher wave

wall. In essence the message is: use the height of the wave wall Rc and not the height of

the armoured crest Ac in Equations 6.5 and 6.6 if the wall is higher than the crest. For a

wave wall lower than the crest armour the height of this crest armour should be used. The

Neural Network prediction might be able to give more precise predictions.

6.3.6 Scale and model effect corrections

Results of the recent CLASH project suggested significant differences between field and

model results on wave overtopping. This has been verified for different sloping rubble

structures. Results of the comparisons in this project have led to a scaling procedure

which is mainly dependent on the roughness of the structure γf [-]; the seaward slope cot α

of the structure [-]; the mean overtopping discharge, up-scaled to prototype, qss [m3/s/m];

and whether wind is considered or not.

Data from the field are naturally scarce, and hence the method can only be regarded as

tentative. It is furthermore only relevant if mean overtopping rates are lower than 1.0 l/s/m

but may include significant adjustment factors below these rates. Due to the inherent

uncertainties, the proposed approach tries to be conservative. It has however been

applied to pilot cases in CLASH and has proved good corrections with these model data.

The adjustment factor fq for model and scale effects can be determined as follows:

/s/mm10for;2logmin

/s/mm10for0.1

max,

ssqss

ss q qfq

q f 6.12

where fq,max is an upper bound to the adjustment factor fq and can be calculated as follows:

9.0for0.1

9.07.0for115.415

7.0for

max,

f frqrqf

frq

q ff

f f

and fq,r is the adjustment factor for rough slopes which is mainly dependent on the slope of

the structure and whether wind needs to be included or not.

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0.4cotfor30

0.4cot6.0for0.4cot5.8

6.0cotfor0.1

w wrq

f ff 6.14

in which fw accounts for the presence of wind and is set to fw = 1.0 if there is wind and

fw = 0.67 if there is no wind.

This set of equations include the case of smooth dikes which will – due to γf = 0.9 in this

case – always lead to an adjustment factor of fq = 1.0. In case of a very rough 1:4 slope

with wind fq,max = fqr = 30.0 which is the maximum the factor can get to (but only if the

mean overtopping rates gets below qss = 10-5 m3/s/m). The latter case and a steep rough

slope is illustrated in Figure 6.8.

qss [m3/s/m]

fq

Zeebrugge (1:1.4)

Ostia (1:4)

Eq. (6.???), f_q,max = 7.9

Eq. (6.???), f_q,max = 30

Figure 6.10: Proposed adjustment factor applied to data from two field sites (Zeebrugge 1:1.4

rubble mound breakwater, and Ostia 1:4 rubble slope)

6.4 Overtopping volumes per wave

Wave overtopping is a dynamic and irregular process and the mean overtopping

discharge, q, does not cover this aspect. But by knowing the storm duration, t, and the

number of overtopping waves in that period, Now, it is easy to describe this irregular and

dynamic overtopping, if the overtopping discharge, q, is known. Each overtopping wave

gives a certain overtopping volume of water, V. The general distribution of overtopping

volumes for coastal structures has been described in Section 4.2.2.

As with many equations in this manual, the two-parameter Weibull distribution describes

the behaviour quite well. This equation has a shape parameter, b, and a scale parameter,

a. For smooth sloping structures an average value of b = 0.75 was found to indicate the

distribution of overtopping volumes (see Section 5.4). The same average value will be

used for rubble mound structures, which makes smooth and rubble mound structures

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easily comparable. The exceedance probability, PV, of an overtopping volume per wave is

then similar to Equations 4.2 and 4.3.

exp1

a

with:

owowwm

ov m NtqNNqTP

Equation 6.16 shows that the scale parameter depends on the overtopping discharge, but

also on the mean period and probability of overtopping, or which is similar, on the storm

duration and the actual number of overtopping waves.

The probability of wave overtopping for rubble mound structures has been described in

Section 6.2, Figure 6.4 and Equation 6.4.

Equations for calculating the overtopping volume per wave for a given probability of

exceedance, is given by Equation 5.34. The maximum overtopping during a certain event

is fairly uncertain, as most maxima, but depends on the duration of the event. In a 6

hours period one may expect a larger maximum than only during 15 minutes. The

maximum during an event can be calculated by Equation 5.35.

6.5 Overtopping velocities and spatial distribution

The hydraulic behaviour of waves on rubble mound slopes and on smooth slopes like

dikes, is generally based on similar formulae, as clearly shown in this chapter. This is

different, however, for overtopping velocities and spatial distribution of the overtopping

water. A dike or sloping impermeable seawall generally has an impermeable and more or

less horizontal crest. Up-rushing and overtopping waves flow over the crest and each

overtopping wave can be described by a maximum velocity and flow depth, see

Section 5.5. These velocities and flow depths form the description of the hydraulic loads

on crest and inner slope and are part of the failure mechanism “failure or erosion of inner

slopes by wave overtopping”.

This is different for rubble mound slopes or breakwaters where wave energy is dissipated

in the rough and permeable crest and where often overtopping water falls over a crest wall

onto a crest road or even on the rear slope of a breakwater. A lot of overtopping water

travels over the crest and through the air before it hits something else.

Only recently in CLASH and a few other projects at Aalborg University attention has been

paid to the spatial distribution of overtopping water at breakwaters with a crest wall (Lykke

Andersen and Burcharth, 2006). The spatial distribution was measured by various trays

behind the crest wall. Figure 6.11 gives different cross-sections with a set-up of three

arrays. Up to six arrays have been used. The spatial distribution depends on the level

with respect to the rear side of the crest wall and the distance from this rear wall, see

Figure 6.12. The coordinate system (x, y) starts at the rear side and at the top of the crest

wall, with the positive y-axis downward.

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Figure 6.11: Definition of y for various cross-sections

Figure 6.12: Definition of x- and y-coordinate for spatial distribution

The exceedance probability F of the travel distance is defined as the volume of

overtopping water passing a given x- and y-coordinate, divided by the total overtopping

volume. The probability, therefore, lies between 0 and 1, with 1 at the crest wall. The

spatial distribution can be described with the following equations, which have slightly been

rewritten and modified with respect to the original formulae by Lykke Andersen and

Burcharth (2006). The probability F at a certain location can be described by:

cos

max.3.1exp, 15.0

op m ysx

yxF

Equation 6.17 can be rewritten to calculate the travel distance x directly (at a certain

level y) by rewriting the above equation:

15.00 7.2)ln(77.0cos opm

ysFHx +−=

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Suppose cosβ = 0, then we get:

F = 0.1 x = 1.77 Hs

F = 0.01 x = 3.55 Hs

It means that 10% of the volume of water travels almost two wave heights through the air

and 1% of the volume travels more than 3.5 times the wave height. These percentages

will be higher if y ≠ 0, which is often the case with a crest unit.

The validity of Equations 6.17 and 6.18 is for rubble mound slopes of approximately 1:2

and for angles of wave attack between 0˚ ≤ |β| < 45˚. It should be noted that the equation

is valid for the spatial distribution of the water through the air behind the crest wall. All

water falling on the basement of the crest unit will of course travel on and will fall into the

water behind and/or on the slope behind.

6.6 Overtopping of shingle beaches

Shingle beaches differ from the armoured slopes principally in the size of the beach

material, and hence its mobility. The typical stone size is sufficiently small to permit

significant changes of beach profile, even under relatively low levels of wave attack. A

shingle beach may be expected to adjust its profile to the incident wave conditions,

provided that sufficient beach material is available. Run-up or overtopping levels on a

shingle beach are therefore calculated without reference to any initial slope.

The equilibrium profile of shingle beaches under (temporary constant) wave conditions is

described by Van der Meer (1988). The most important profile parameter for run-up and

overtopping is the crest height above SWL, hc. For shingle with Dn50 < 0.1 m this crest

height is only a function of the wave height and wave steepness. Note that the mean

wave period is used, not the spectral wave period Tm-1,0.

−= ommc sHh

Only the highest waves will overtop the beach crest and most of this water will percolate

through the material behind the beach crest. Equation 6.19 gives a run-up or overtopping

level which is more or less close to Ru2%.

6.7 Uncertainties

Since wave overtopping formulae are principally identical to the ones for sea dikes,

uncertainties of the models proposed in this chapter should be dealt with in the same way

as those proposed in section 5.8 already.

It should however be noted that some of the uncertainties of the relevant parameters

might change. For rubble mound structures the crest height is about 30% more uncertain

than for smooth dikes and will result in about 0.08 m. Furthermore, the slope uncertainty

increases by about 40% to 2.8%. All uncertainties related to waves and water levels will

remain as discussed within section 5.8.

The minor changes in these uncertainties will not affect the lines as shown in Figure 5.43.

Hence, the same proposal accounting for uncertainties as already given in Section 5.8 is

applied here.

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Again, it should be noted that only uncertainties for mean wave overtopping rates are

considered here. Other methods as discussed in this chapter were disregarded but can be

dealt with using the principal procedure as discussed in Section 1.5.4.

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7.1 Introduction

This chapter presents guidance for the assessment of overtopping and post-overtopping

processes at vertical and steep-fronted coastal structures such as caisson and blockwork

breakwaters and vertical seawalls (Figure 7.1, Figure 7.2 ). Also included are composite

vertical wall structures (where the emergent part of the structure is vertical, fronted by a

modest berm) and vertical structures which include a recurve / bull-nose / parapet / wave

return wall as the upper part of the defence.

Large vertical breakwaters (Figure 7.1) are almost universally formed of sand-filled

concrete caissons usually resting on a small rock mound. Such caisson breakwaters may

reach depths greater than 100m, under which conditions no wave breaking at all at the

wall would be expected. Conversely, older breakwaters may, out of necessity, have been

constructed in shallower water or indeed, built directly on natural rock “skerries”. As such,

these structures may find themselves exposed to breaking wave, or “impulsive” conditions

when the water depth in front of them is sufficiently low. Urban seawalls (e.g. Figure 7.2)

are almost universally fronted by shallow water, and are likely to be exposed to breaking

or broken wave conditions, especially in areas of significant tidal range.

Figure 7.1: Examples of vertical breakwaters: (left) modern concrete caisson and (right) older

structure constructed from concrete blocks

Figure 7.2: Examples of vertical seawalls: (left) modern concrete wall and (right) older stone

blockwork wall

There are three principal sources of guidance on this topic preceding this manual; in the

UK, the Environment Agency “Overtopping of Seawalls: Design and Assessment Manual”

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(EA / Besley, 1999); in the U.S.A., the US Army Corps of Engineers’ “Coastal Engineering

Manual” (CEM / Burcharth & Hughes, 2002); in Japan, Goda’s design charts (e.g. Goda,

2000). The guidance presented in this chapter builds upon that of EA / Besley (1999),

with adjustments to many formulae based upon further testing since 1999.

For those familiar with EA / Besley (1999), the principal changes / additions are

• new guidance on prediction of mean and wave-by-wave overtopping to oblique

wave attack under impulsive conditions (Section 7.3.4);

• extension of method for mean overtopping to account for steep (but not vertical)

“battered” walls (Section 7.3.2);

• new guidance on mean overtopping under conditions when all waves break before

reaching the wall (part of Section 7.3.1);

• new guidance on reduction in mean overtopping discharge due to wave return

walls / parapets / recurves (Section 7.3.5);

• new guidance on “post-overtopping” processes, specifically; velocity of “throw”;

landward spatial extent of overtopping, and effect of wind (Section 7.3.6)

• inclusion of summary of new evidence on scale effects for laboratory study of

overtopping at vertical and steep walls (Section 7.3.7).

• minor adjustments to recommended approach for distinguishing impulsive / nonimpulsive conditions (Section 7.2);

• minor adjustments to formulae for mean overtopping under impulsive conditions

due to the availability of additional data, from e.g. the CLASH database

(Section 7.3.1).

• all formulae are now given in terms of wave period Tm-1,0 resulting in an adjusted

definition of the h* and d* parameters (Sections 7.2.2 and 7.2.3 respectively) in

order to maintain comparability with earlier work.

• in line with convergence on the Tm-1,0 measure, formulae using wave steepness sop

have been adjusted to use the new preferred measure sm-1,0 (Section 7.3.1);

• all formulae are now given explicitly in terms of basic wave and structural

parameters without recourse to intermediate definitions of dimensionless

overtopping discharge and freeboard parameters specific to impulsive conditions.

This chapter follows approximately the same sequence as the preceding two chapters,

though certain differences should be noted. In particular, run-up is not addressed, as it is

not a measure of physical importance for this class of structure – indeed it is not welldefined for cases when the wave breaks, nearly-breaks or is broken when it reaches the

structure, under which conditions an up-rushing jet of water is thrown upwards.

The qualitative form of the physical processes occurring when the waves reach the wall

are described in Section 7.2. Distinctions drawn between different wave / structure

“regimes” are reflected in the guidance for assessment of mean overtopping discharges

given in Section 7.3. The basic assessment tools are presented for plain vertical walls

(Section 7.3.1), followed by subsections giving advice on how these basic tools should be

adjusted to account for other commonly-occurring configurations; battered walls

(Section 7.3.2); vertically composite walls (Section 7.3.3); the effect of oblique wave attack

(Section 7.3.4); the effect of recurve / wave-return walls (Section 7.3.5). Scale and model

effects are reviewed in Section 7.3.7. Methods to assess individual “wave by wave”

overtopping volumes are presented in Section 7.4. The current knowledge and advice on

post-overtopping processes including velocities, spatial distributions and post-overtopping

loadings are reviewed in Section 7.5.

Principal calculation procedures are summarised in Table 7.1

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Table 7.1: Summary of principal calculation procedures for vertical structures

Deterministic design Probabilistic design

Discrimination – impulsive / non-impulsive regime

plain vertical walls Eq. 7.1

vertical composite walls Eq. 7.2

Plain vertical walls

non-impulsive conditions Eq. 7.4 Eq. 7.3

impulsive conditions Eq. 7.6 Eq. 7.5

broken wave conditions (submerged toe) Eq. 7.8 Eq. 7.7

broken wave conditions (emergent toe) Eq. 7.10 Eq. 7.9

Battered walls Eq. 7.11 Eq. 7.11

Composite vertical walls Eq. 7.13 Eq. 7.12

Oblique wave attack

non-impulsive conditions Eq. 7.14 & 7.15

impulsive conditions Eq. 7.17 Eq. 7.18

Vertical walls with wave return wall / parapet Eqs. 7.18, 7.19 & Fig. 7.20

Effect of wind Eq. 7.20 & 7.21

Percentage of overtopping waves Eq. 7.22 / 7.23

with oblique waves Eqs.7.29 & 7.30

Individual overtopping volumes Eqs.7.24 to 7.28

with oblique waves Table 7.2

Overtopping velocities Eq. 7.31

Spatial extent of overtopping Fig. 7.25

Downfall pressures due to overtopped discharge Eq. 7.32

7.2 Wave processes at walls

7.2.1 Overview

In assessing overtopping on sloping structures, it is necessary to distinguish whether

waves are in the “plunging” or “surging” regime (Section 5.3.1). Similarly, for assessment

of overtopping at steep-fronted and vertical structures the regime of the wave / structure

interaction must be identified first, with quite distinct overtopping responses expected for

each regime.

On steep walls (vertical, battered or composite), “non-impulsive” or “pulsating” conditions

occur when waves are relatively small in relation to the local water depth, and of lower

wave steepnesses. These waves are not critically influenced by the structure toe or

approach slope. Overtopping waves run up and over the wall giving rise to (fairly)

smoothly-varying loads and “green water” overtopping (Figure 7.3).

In contrast, “impulsive” conditions (Figure 7.4) occur on vertical or steep walls when

waves are larger in relation to local water depths, perhaps shoaling up over the approach

bathymetry or structure toe itself. Under these conditions, some waves will break violently

against the wall with (short-duration) forces reaching 10 − 40 times greater than for nonimpulsive conditions. Overtopping discharge under these conditions is characterised by a

“violent” uprushing jet of (probably highly aerated) water.

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Figure 7.3: A non-impulsive (pulsating) wave condition at a vertical wall, resulting in non-impulsive

(or “green water”) overtopping

Figure 7.4: An impulsive (breaking) wave at a vertical wall, resulting in an impulsive (violent)

overtopping condition

Lying in a narrow band between non-impulsive and impulsive conditions are “nearbreaking” conditions where the overtopping is characterised by suddenness and a highspeed, near vertical up-rushing jet (like impulsive conditions) but where the wave has not

quite broken onto the structure and so has not entrained the amount of air associated with

fully impulsive conditions. This “near-breaking” condition is also known as the “flip

through” condition. This conditions gives overtopping in line with impulsive (breaking)

conditions and are thus not treated separately.

Many seawalls are constructed at the back of a beach such that breaking waves never

reach the seawall, at least not during frequent events where overtopping is of primary

importance. For these conditions, particularly for typical shallow beach slopes of less than

(say) 1:30, design wave conditions may be given by waves which start breaking (possibly

quite some distance) seaward of the wall. These “broken waves” arrive at the wall as a

highly-aerated mass of water (Figure 7.5), giving rise to loadings which show the sort of

short-duration peak seen under impulsive conditions (as the leading edge of the mass of

water arrives at the wall) but smaller in magnitude due to the high level of aeration. For

cases where the depth at the wall hs > 0, overtopping can be assessed using the method

for impulsive conditions. For conditions where the toe of the wall is emergent (hs ≤ 0),

these methods can no longer be applied and an alternative is required (Section 7.3.1).

Figure 7.5: A broken wave at a vertical wall, resulting in a broken wave overtopping condition

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In order to proceed with assessment of overtopping, it is therefore necessary first to

determine which is the dominant overtopping regime (impulsive or non-impulsive) for a

given structure and design sea state. No single method gives a discriminator which is

100% reliable. The suggested procedure for plain and composite vertical structures

includes a transition zone in which there is significant uncertainty in the prediction of

dominant overtopping regime and thus a “worst-case” is taken.

7.2.2 Overtopping regime discrimination – plain vertical walls

Hm0

Rc = crest freeboard

Hm0 = wave height at the toe of the structure

hs = water depth at the toe of the structure

α = slope angle of foreshore

Rc hs foreshore slope 1:m

Figure 7.6: Definition sketch for assessment of overtopping at plain vertical walls

This method is for distinguishing between impulsive and non-impulsive conditions at a

vertical wall where the toe of the wall is submerged (hs> 0; Figure 7.6). When the toe of

the wall is emergent (hs < 0) only broken waves reach the wall.

For submerged toes (hs> 0), a wave breaking or “impulsiveness” parameter, h* is defined

based on depth at the toe of the wall, hs, and incident wave conditions inshore:

m s m s Tg h

hh π 7.1

Non-impulsive (pulsating) conditions dominate at the wall when h* > 0.3, and impulsive

conditions occur when h* < 0.2. The transition between conditions for which the

overtopping response is dominated by breaking and non-breaking waves lies over 0.2 ≤ h*

≤ 0.3. In this region, overtopping should be predicted for both non-impulsive and

impulsive conditions, and the larger value assumed.

7.2.3 Overtopping regime discrimination – composite vertical walls

For vertical composite walls where a berm or significant toe is present in front of the wall,

an adjusted version of the method for plain vertical walls should be used. A modified

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“impulsiveness” parameter, d*, is defined in a similar manner to the h* parameter (for plain

vertical walls, Section 7.2.2);

m s m Tg

h

dd π 7.2

with parameters defined according to Figure 7.7.

Hm0

Rc = crest freeboard

Hm0 = wave height at the toe of the structure

hs = water depth at the toe of the structure

d = water depth above the berm of the structure

Rc d hs Figure 7.7: Definition sketch for assessment of overtopping at composite vertical walls

Non-impulsive conditions dominate at the wall when d* > 0.3, and impulsive conditions

occur when d* < 0.2. The transition between conditions for which the overtopping

response is dominated by breaking and non-breaking waves lies over 0.2 ≤ d* ≤ 0.3. In

this region, overtopping should be predicted for both non-impulsive and impulsive

conditions, and the larger value assumed.

7.3 Mean overtopping discharges for vertical and battered walls

7.3.1 Plain vertical walls

For simple vertical breakwaters under the following equations should be used:

Probabilistic design, non-impulsive conditions (h* > 0.3): The mean prediction should

be used for probabilistic design, or for comparison with measurements (Equation 7.3).

The coefficient of 2.6 for the mean prediction has an associated standard deviation of

6.2exp04.0

m c m

gH q valid for 0.1 < Rc/Hm0 < 3.5 7.3

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Deterministic design or safety assessment, non-impulsive conditions (h* > 0.3): For

deterministic design or safety assessment, the following equation incorporates a factor of

safety of one standard deviation above the mean prediction:

8.1exp04.0

m c m

gH q valid for 0.1 < Rc/Hm0 < 3.5 7.4

dimensionless freeboard Rc/Hm0

di m en si on le ss d is ch ar ge q /(g

m

CLASH database set 028

CLASH database set 106

CLASH database set 224

CLASH database set 225

CLASH database set 351

CLASH database set 402

CLASH database set 502

plain vertical - probabilistic (Eq. 7.3)

plain vertical - deterministic (Eq. 7.4)

Figure 7.8: Mean overtopping at a plain vertical wall under non-impulsive conditions

(Equations 7.3 and 7.4)

Zero Freeboard: For a vertical wall under non-impulsive conditions Equation 7.5 should

be used for probabilistic design and for prediction and comparison of measurements

(Figure 5.13) Smid (2001)

Hg q

m0 ±= valid for Rc/Hm0 = 0 7.5

For deterministic design or safety assessment it is recommended to increase the average

overtopping discharge in Equation 7.5 by one standard deviation.

No data are available for impulsive overtopping at zero freeboard at vertical walls.

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q/ (g

q/(g.HS

Figure 7.9: Dimensionless overtopping discharge for zero freeboard (Smid, 2001)

Probabilistic design, impulsive conditions (h* ≤ 0.2): The mean prediction should be

used for probabilistic design, or for comparison with measurements (Equation 7.6). The

scatter in the logarithm of the data about the mean prediction is characterised by a

standard deviation of c. 0.37 (i.e. c. 68% of predictions lie within a range of ×/÷ 2.3).

m c s

Rh ghh

q valid over 0.03 <

m c

Deterministic design or safety assessment, impulsive conditions (h* ≤ 0.2): For

deterministic design or safety assessment, the following equation incorporates a factor of

safety of one standard deviation above the mean prediction:

m c s

Rh ghh

q valid over 0.03 <

m c

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(impulsive) dimensionless freeboard h* Rc/Hm0

di m en si on le ss d is ch ar ge q

h

(g h s

5 CLASH database set 028 CLASH database set 224

CLASH database set 225 CLASH database set 351

CLASH database set 502 CLASH database set 802

plain vertical - probabilistic (Eq. 7.5) plain vertical - deterministic (Eq. 7.6)

Figure 7.10: Mean overtopping at a plain vertical wall under impulsive conditions (Equations 7.6

and 7.7)

For Rh < 0.02 arising from hs reducing to very small depths (as opposed to from small

relative freeboards) there is evidence supporting an adjustment downwards of the

predictions of the impulsive formulae due to the observation that only broken waves arrive

at the wall (Bruce et al., 2003). For probabilistic design or comparison with

measurements, the mean prediction should be used (Equation 7.8). The scatter in the

logarithm of the data about the mean prediction is characterised by a standard deviation

of c. 0.15 (i.e. c. 68% of predictions lie within a range of ×/÷ 1.4).

* sghh

q

m c

h valid for

m c

h < 0.02; broken waves 7.8

For deterministic design or safety assessment, the following equation incorporates a

factor of safety of one standard deviation (in the multiplier) above the mean prediction:

* sghh

q

m c

h valid for

m c

h < 0.02; broken waves 7.9

For 0.02 < h* Rc / Hm0 < 0.03, there appears to be a transition between Equation 7.7 (for

“normal” impulsive conditions) and Equation 7.8 (for conditions with only broken waves).

There is however insufficient data upon which to base a firm recommendation in this

range. It is suggested that Equation 7.7 is used down to h* Rc / Hm0 = 0.02 unless it is

clear that only broken waves will arrive at the wall, in which case Equation 7.8 could be

used. Formulae for these low h* Rc / Hm0 conditions are shown in Figure 7.11.

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(impulsive) dimensionless freeboard h* Rc / Hm0

di m en si on le ss d is ch ar ge q

h

(g h s

5 Bruce et al (2003) data

broken waves only- probabilistic (Eq. 7.7)

broken waves only - deterministic (Eq. 7.8)

breaking waves - probabilistic (Eq. 7.5)

Figure 7.11: Mean overtopping discharge for lowest h* Rc / Hm0 (for broken waves only arriving at

wall) with submerged toe (hs > 0). For 0.02 < h* Rc / Hm0 < 0.03, overtopping response

is ill-defined – lines for both impulsive conditions (extrapolated to lower h* Rc / Hm0)

and broken wave only conditions (extrapolated to higher h* Rc / Hm0) are shown as

dashed lines over this region

Data for configurations where the toe of the wall is emergent (i.e. at or above still water

level, hs ≤ 0) is limited. The only available study suggests an adaptation of a prediction

equation for plunging waves on a smooth slope may be used, but particular caution

should be exercised in any extrapolation beyond the parameter ranges of the study, which

only used a relatively steep (m =10) foreshore slope.

For probabilistic design or comparison with measurements, the mean prediction

should be used (Equation 7.10) should be used. The standard deviation associated with

the exponent coefficient (−2.16) is c. 0.21.

deepm

c mm deepm

Rsmsm

gH q

16.2exp043.0

valid for 2.0 <

deepm

c m H

Rsm

0,1− < 5.0; 0.55 ≤ Rc/Hm0,deep ≤ 1.6;

sm-1,0 ≥ 0.025; Note – data only available for m=10 (i.e. 1:10 foreshore

slope)

For deterministic design or safety assessment, Equation 7.11 incorporates a factor of

safety of one standard deviation (in the exponent) above the mean prediction.

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deepm

c mm deepm

Rsmsm

gH q

95.1exp043.0

valid for 2.0 <

deepm

c m H

Rsm

0,1− < 5.0; 0.55 ≤ Rc/Hm0,deep ≤ 1.6;

sm-1,0 ≥ 0.025; NB – data only available for m=10 (i.e. 1:10 foreshore slope)

Equations 7.10 and 7.11 for overtopping under emergent toe conditions are illustrated in

Figure 7.12. It should be noted that this formula is based upon a limited dataset of

small-scale tests with 1:10 foreshore only and should not be extrapolated beyond the

ranges tested (foreshore slope 1:m = 0.1; sop ≥ 0.025; 0.55 ≤ Rc/Hm0,deep ≤ 1.6).

dimensionless freeboard Rc/Hm0 x sm-1,00.33 x m

di m 'le

ss d is ch ar ge q /(g

m

s m

x m

Bruce et al (2003) data

emergent toe - probabilistic (Eq. 7.9)

emergent toe - deterministic (Eq. 7.10)

Figure 7.12: Mean overtopping discharge with emergent toe (hs < 0)

7.3.2 Battered walls

Near-vertical walls with 10:1 and 5:1 batters are found commonly for older UK seawalls

and breakwaters (e.g. Figure 7.13).

Mean overtopping discharges for battered walls under impulsive conditions are slightly in

excess of those for a vertical wall over a wide range of dimensionless freeboards.

Multiplying factors are given in Equation 7.12 (plotted in Figure 7.14).

10:1 battered wall: q10:1 batter = qvertical × 1.3 5:1 battered wall: q5:1 batter = qvertical × 1.9

where qvertical is arrived at from Equation 7.6 (for probabilistic design) or Equation 7.7 (for

deterministic design). The uncertainty in the final estimated overtopping discharge can be

estimated as per the plain vertical cases.

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Figure 7.13: Battered walls: typical cross-section (left), and Admiralty Breakwater, Alderney

Channel Islands (right, courtesy G.Müller)

(impulsive) dimensionless freeboard, h* Rc/Hm0

di m en si on le ss d is ch ar ge q

h

(g h s

plain vertical (Eq. 7.5)

10:1 batter (Eq. 7.11)

5:1 batter (Eq. 7.11)

Figure 7.14: Overtopping for a 10:1 and 5:1 battered walls

No dataset is available to indicate an appropriate adjustment under non-impulsive

conditions. Given that these battered structures are generally older structures in

shallower water, it is likely that impulsive conditions are possible at most, and will form the

design case.

7.3.3 Composite vertical walls

It is well-established that a relatively small toe berm can change wave breaking

characteristics, thus substantially altering the type and magnitude of wave loadings (e.g.

(Oumeraci et al., 2001). Many vertical seawall walls may be fronted by rock mounds with

the intention of protecting the toe of the wall from scour. The toe configuration can vary

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considerably, potentially modifying the overtopping behaviour of the structure. Three

types of mound can be identified

1. Small toe mounds which have an insignificant effect on the waves approaching the

wall – here the toe may be ignored and calculations proceed as for simple vertical

(or battered) walls.

2. Moderate mounds, which significantly affect wave breaking conditions, but are still

below water level. Here a modified approach is required.

3. Emergent mounds in which the crest of the armour protrudes above still water

level. Prediction methods for these structures may be adapted from those for

crown walls on a rubble mound (Section 6.3.5).

For assessment of mean overtopping discharge at a composite vertical seawall or

breakwater, the overtopping regime (impulsive / non-impulsive) must be determined – see

Section 7.2.3.

When non-impulsive conditions prevail, overtopping can be predicted by the standard

method given previously for non-impulsive conditions at plain vertical structures,

Equation 7.3.

For conditions determined to be impulsive, a modified version of the impulsive prediction

method for plain vertical walls is recommended, accounting for the presence of the mound

by use of d and d*.

For probabilistic design or comparison with measurements, the mean prediction

(Equation 7.13) should be used. The scatter in the logarithm of the data about the mean

prediction is characterised by a standard deviation of c. 0.28 (i.e. c. 68% of predictions lie

within a range of ×/÷ 1.9).

m c s

Rd ghd

q valid for 0.05 <

m c

d < 1.0 and h* < 0.3

For deterministic design or safety assessment, Equation 7.14 incorporates a factor of

safety of one standard deviation (in the constant multiplier) above the mean prediction.

m c s

Rd ghd

q valid for 0.05 <

m c

d < 1.0 and h* < 0.3

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(impulsive, composite) dimensionless freeboard d* Rc/Hm0

di m en si on le ss d is ch ar ge q

d

(g h s

5 VOWS data

composite vertical - probabilistic (Eq. 7.12)

composite vertical - deterministic (Eq. 7.13)

Figure 7.15: Overtopping for composite vertical walls

7.3.4 Effect of oblique waves

Seawalls and breakwaters seldom align perfectly with incoming waves. The assessment

methods presented thus far are only valid for shore-normal wave attack. In this

subsection, advice on how the methods for shore-normal wave attack (obliquity β = 0°)

should be adjusted for oblique wave attack.

This chapter extends the existing design guidance for impulsive wave attack from

perpendicular to oblique wave attack. As for zero obliquity, overtopping response

depends critically upon the physical form (or “regime”) of the wave / wall interaction – nonimpulsive; impulsive or broken. As such, the first step is to use the methods given in

Section 7.2 to determine the form of overtopping for shore-normal (zero obliquity). Based

upon the outcome of this, guidance under “non-impulsive conditions” or “impulsive

conditions” should be followed.

For non-impulsive conditions, an adjusted version of Equation 7.3 should be used

(Equation 7.15):

6.2exp04.0

m c m

gH q

where γ is the reduction factor for angle of attack and is given by

and β is the angle of attack relative to the normal, in degrees.

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For conditions that would be identified as impulsive for normal (β = 0°) wave attack, a

more complex picture emerges (Napp et al., 2004). Diminished incidence of impulsive

overtopping is observed with increasing obliquity (angle β) of wave attack. This results

not only in reductions in mean discharge with increasing β but also, for β ≥ 60°, a switch

back over to the functional form observed for non-impulsive conditions (i.e. a move away

from a power-law decay such as Equation 7.6 to an exponential one such as

Equation 7.3).

(impulsive) dimensionless freeboard, h* Rc/Hm0

di m en si on le ss d is ch ar ge q

h

(g h s

beta = 0 degrees (Eq. 7.5)

beta = 15 degrees (Eq. 7.16)

beta = 30 degrees (Eq. 7.16)

Figure 7.16: Overtopping of vertical walls under oblique wave attack

For probabilistic design or comparison with measurements, the mean predictions

should be used (Equation 7.17) should be used. Data only exist for the discrete values of

obliquity listed.

for β = 15° ;

m c

h ≥ 0.2

m c s

Rh ghh

q for β = 15° ;

m c

h < 0.2 as per impulsive β = 0° (Eq. 7.6)

for β = 30 °;

m c

h ≥ 0.07

m c s

Rh ghh

q for β = 60 °;

m c

h ≥ 0.07 as per non-impulsive β=60° (Eq.7.16)

Significant spatial variability of overtopping volumes along the seawall under oblique wave

attack are observed / measured in physical model studies. For deterministic design,

Equation 7.18 should be used, as these give estimates of the “worst case” conditions at

locations along the wall where the discharge is greatest.

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for β = 150 ;

m c

h ≥ 0.2 as per impulsive β = 0° (Eq. 7.7)

for β = 30 0;

m c

h ≥ 0.07 as per impulsive β = 15° (Eq. 7.17)

for β = 60 0;

m c

h ≥ 0.07 as per non-impulsive β = 0° (Eq. 7.4)

7.3.5 Effect of bullnose and recurve walls

Designers of vertical seawalls and breakwaters have often included some form of

seaward overhang (recurve / parapet / wave return wall / bullnose) as part of the structure

with the design motivation of reducing wave overtopping by deflecting back seaward

uprushing water (eg Figure 7.18). The mechanisms determining the effectiveness of a

recurve are complex and not yet fully described. The guidance presented here is based

upon physical model studies (Kortenhaus et al., 2003; Pearson et al., 2004).

Parameters for the assessment of overtopping at structures with bullnose / recurve walls

are shown in Figure 7.19.

Figure 7.17: An example of a modern, large vertical breakwater with wave return wall (left) and

cross-section of an older seawall with recurve (right)

Figure 7.18: A sequence showing the function of a parapet / wave return wall in reducing

overtopping by redirecting the uprushing water seaward (back to right)

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Hm0

Rc = crest freeboard

Pc = height of vertical part of wall

hr = height of wave return wall / parapet

α = angle of wave return wall / parapet

Br = horizontal extension of wave return

wall / parapet in front of main wall

Hm0 = wave height at the toe of structure

hs = water depth at the toe of structure

Rc hs Pc Br hr α

Figure 7.19: Parameter definitions for assessment of overtopping at structures with parapet / wave

return wall

Two conditions are distinguished;

• the familiar case of the parapet / bullnose / recurve overhanging seaward (α <

90°), and

• the case where a wall is chamfered backwards at the crest (normally admitting

greater overtopping (α > 90°).

For the latter, chamfered wall case, Cornett influence factors γ should be applied to

Franco’s equation for non-impulsive mean discharge (Equation 7.19) with a value of γ

selected as shown (Cornett et al., 1999)

3.4exp2.0

m c m

gH q

For the familiar case of overhanging parapet / recurve / bullnose, the effectiveness of the

recurve / parapet in reducing overtopping is quantified by a factor k defined as

curvewithout_re

vewith_recur

q q k = 7.20

The decision chart in Figure 7.20 can then be used to arrive at a value of k, which in turn

can be applied by multiplication to the mean discharge predicted by the most appropriate

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method for the plain vertical wall (with the same Rc , hs etc.). The decision chart shows

three levels of decision;

• whether the parapet is angled seaward or landward;

• if seaward (α < 90º), whether conditions are in the small (left box),

intermediate (middle box) or large (right box) reduction regimes;

• if in the regime of largest reductions (greatest parapet effectiveness;

Rc/Hm0 ≥ R0* + m* ), which of three further sub-regimes (for different Rc / hs)

is appropriate.

Given the level of scatter in the original data and the observation that the methodology is

not securely founded on the detailed physical mechanisms / processes, it is suggested

that it is impractical to design for k < 0.05, i.e. reductions in mean discharges by factors of

greater than 20 cannot be predicted with confidence. If such large (or larger) reductions

are required, a detailed physical model study should be considered.

Figure 7.20: “Decision chart” summarising methodology for tentative guidance. Note that symbols

R0*, k23, m and m* used (only) at intermediate stages of the procedure are defined in

the lowest boxes in the figure. Please refer to text for further explanation.

refer to

Cornett et al (1999)

m c ≤ **0

0 mRH

m c +<< **0

mR

m c +≥

1=k ⎟

m k m c

Rkk

m c

s c h

s c h

s c h

kk ′= ⎟

s c h Rkk 5.8exp180

for all k < 0.05

k < 0.05 may not safely

be realisable in design

− consider physical

model tests

c c r r

c c r r

hm 2.01.1 +×=

( )23* 1 kmm −=

k23 = 0.2

recommended

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7.3.6 Effect of wind

Wind may affect overtopping processes and thus discharges by:

• changing the shape of the incident wave crest at the structure resulting in a

possible modification of the dominant regime of wave interaction with the wall;

• blowing up-rushing water over the crest of the structure (for an onshore wind, with

the reverse effect for an offshore wind) resulting in possible modification of mean

overtopping discharge and wave-by-wave overtopping volumes;

• modifying the physical form of the overtopping volume or jet, especially in terms of

its aeration and break-up resulting in possible modification to post-overtopping

characteristics such as throw speed, landward distribution of discharge and any

resulting post-overtopping loadings (e.g. downfall pressures).

The modelling of any of these effects in small-scale laboratory tests presents very great

difficulties owing to fundamental barriers to the simultaneous scaling of the wave-structure

and water-air interaction processes. Very little information is available to offer guidance

on effect (1) – the reshaping of the incident waves. Comparisons of laboratory and field

data (both with and without wind) have enabled some upper (conservative) bounds to be

placed upon effect (2) – the intuitive wind-assistance in “pushing” of up-rushing water

landward across the crest. These are discussed immediately below. Discussion of

effect (3) – modification to “post-overtopping” processes – is reserved for Sections 7.5.3

and 7.5.4 (on distributions and downfalling pressures respectively).

For vertical structures, several investigations on vertical structures have suggested

different adjustment factors fwind ranging from 30% to 40% to up to 300% (Figure 7.21)

either using a paddle wheel or large fans to transport uprushing water over the wall.

qss [m3/s/m]

fW in d

de Waal et al. (1996)

Davey (2004)

Pullen & Allsop (2004)

Eq. (7.??)

Figure 7.21: Wind adjustment factor fwind plotted over mean overtopping rates qss

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When these tests were revisited a simple adjustment factor was proposed for the mean

discharge based upon small-scale tests qss, which is already scaled up by appropriate

scaling to full-scale (see also de Rouck et al., 2005).

log.(30.1

−+= sswind qf

/s/mm10for

/s/mm1010for

/s/mm10for

ss ss ss q q q

From Equation 7.21 it becomes clear that the influence of wind only gets important for

very low overtopping rates below qss = 0.1 l/s/m. Hence, in many practical cases, the

influence of wind may be disregarded. The mean overtopping discharge including wind

becomes

ssqfq ×= windwith wind 7.22

7.3.7 Scale and model effect corrections

Tests in a large-scale wave channel (Figure 7.22) and field measurements (Figure 7.23)

have demonstrated that with the exception of wind effect (Section 7.3.6), results of

overtopping measurements in small-scale laboratory studies may be securely scaled to

full-scale under non-impulsive and impulsive overtopping conditions (Pearson et al., 2002;

Pullen et al., 2004).

No information is yet available on the scaling of small-scale data under conditions where

broken wave attack dominates. Comparison of measurements of wave loadings on

vertical structures under broken wave attack at small-scale and in the field suggests that

prototype loadings will be over-estimated by small-scale tests in the presence of highlyaerated broken waves. Thus, although the methods presented for the assessment of

overtopping discharges under broken wave conditions given in Section 7.3.1 have not

been verified at large-scale or in the field, any scale correction is expected to give a

reduction in predicted discharge.

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(impulsive) dimensionless freeboard, h* Rc/Hm0

di m en si on le ss d is ch ar ge q

h

(g h s

Large-scale data (Pearson et al, 2002)

Eq. 7.11 (10:1 batter)

Figure 7.22: Large-scale laboratory measurements of mean discharge at 10:1 battered wall under

impulsive conditions showing agreement with prediction line based upon small-scale

tests (Equation 7.12)

(impulsive, composite) dimensionless freeboard d* Rc/Hm0

di m en si on le ss d is ch ar ge q

d

(g h s

field data (Pullen et al, 2005)

composite vertical - probabilistic (Eq. 7.12)

composite vertical - deterministic (Eq. 7.13)

Figure 7.23: Results from field measurements of mean discharge at Samphire Hoe, UK, plotted

together with Equation 7.13

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7.4 Overtopping volumes

7.4.1 Introduction

While the prediction of mean discharge (Section 7.3) offers the information required to

assess whether overtopping is slight, moderate or severe, and make a link to any possible

flooding that might result, the prediction of the volumes associated with individual wave

events can offer an alternative (and often more appropriate) measure for the assessment

of tolerable overtopping levels and possible direct hazard. First, a method is given for the

prediction of maximum overtopping volumes expected associated with individual wave

events for plain vertical structures under perpendicular wave attack (Section 7.4.2). This

method is then extended to composite (bermed) structures (Section 7.4.3) and to

conditions of oblique wave attack (Section 7.4.4). Finally, a short section on scale effects

is included (Section 7.4.5). Also refer to Section 4.2.2.

The methods given for perpendicular wave attack are the same as those given previously

in UK guidance (EA / Besley, 1999). Only the extension to oblique wave attack is new.

7.4.2 Overtopping volumes at plain vertical walls

The first step in the estimation of a maximum expected individual wave overtopping

volume is to estimate the number of waves overtopping (Now) in a sequence of Nw incident

waves.

For non-impulsive conditions, this was found to be well-described by (Franco et al.,

21.1exp

m c wow H

RNN (for h* > 0.3) 7.23

(arising from earlier tests on sloping structures in which situation the number of

overtopping waves was directly linked to run-up, in turn linked to a Rayleigh-distributed set

of incident wave heights).

Under impulsive conditions, Now is better described by (EA / Besley, 1999)

c m wow Rh

where h* RC /Hm0 is the dimensionless freeboard parameter for impulsive conditions

(Equation 7.1).

The distribution of individual overtopping volumes in a sequence is generally welldescribed by a two-parameter Weibull distribution (also refer to Section 4.2.2);

b V a

VP exp1 7.25

where PV is the probability that an individual event volume will not exceed V. a and b are

Weibull “shape” and “scale” parameters respectively. Thus, to estimate the largest event

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in a wave sequence predicted to include (e.g.) Now = 200 overtopping events, Vmax would

be found by taking PV = 1/200 = 0.005. Equation 7.25 can then be rearranged to give

( ) bowNaV /1max ln= 7.26

The Weibull shape parameter a depends upon the average volume per overtopping wave

Vbar where

ow wm bar N

NqT

For non-impulsive conditions, there is a weak steepness-dependency for the scale and

shape parameters a and b (Franco (1996);

04.0for 82.0

02.0for 66.0

m m bar

bar

s s b

a (for h* > 0.3) 7.28

For impulsive conditions, (EA / Besley, 1999; Pearson et al., 2002);

barVa 92.0= 85.0=b (for h* < 0.3) 7.29

The effectiveness of the predictor under impulsive conditions can be gauged from Figure

predicted max. individual overtopping volume, Vmax [m3/m]

m ea su re d m ax . i

nd iv id ua l o

ve rt op pi ng vo lu m e,

m ax [m 3 /m

Large-scale data (Pearson et al, 2002)

Small-scale data (Pearson et al, 2002)

Figure 7.24: Predicted and measured maximum individual overtopping volume – small- and largescale tests (Pearson et al., 2002)

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7.4.3 Overtopping volumes at composite (bermed) structures

There is very little information available specifically addressing wave-by-wave overtopping

volumes at composite structures. The guidance offered by EA / Besley (1999) remains

the best available. No new formulae or Weibull a, b values are known so, for the

purposes of maximum overtopping volume prediction, the methods for plain vertical walls

(Section 7.4.2) are used. The key discriminator is that composite structures whose

mound is sufficiently small to play little role in the overtopping process are treated as plain

vertical, non-impulsive, whereas those with large mounds are treated as plain vertical,

impulsive.

For this purpose, the significance of the mound is assessed using the “impulsiveness”

parameter for composite structures, d* (Equation 7.2). “Small mound” is defined as d* >

0.3, with d* < 0.3 being “large mound”.

7.4.4 Overtopping volumes at plain vertical walls under oblique wave attack

For non-impulsive conditions, an adjusted form of Equation 7.23 is suggested (Franco

et al., 1994);

1exp

m c wow H

NN (for h* > 0.3) 7.30

C is given by

o oo o 40for

400for

0for

βC (for h* > 0.3) 7.31

For impulsive conditions (as determined for perpendicular i.e. β = 0° wave attack), the

procedure is the same as for perpendicular (β = 0°) wave attack, but different formulae

should be used for estimating the number of overtopping waves (Now) and Weibull shape

and scale parameters – see Table 7.2 (Napp et al., 2004).

Table 7.2: Summary of prediction formulae for individual overtopping volumes under oblique

wave attack. Oblique cases valid for 0.2 < h* Rc / Hm0 < 0.65. For 0.07 < h* Rc / Hm0 <

0.2, the β = 00 formulae should be used for all β

c m wow Rh

c m wow Rh

HNN treat as non-impulsive

a = 1.06 Vbar a = 1.04 Vbar treat as non-impulsive

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b = 1.18 b = 1.27 treat as non-impulsive

7.4.5 Scale effects for individual overtopping volumes

Measurements from large-scale laboratory tests indicate that formulae for overtopping

volumes, based largely upon small-scale physical model studies, scale well (Figure 7.24)

(Pearson et al., 2002). No data from the field is available to support “scale-ability” from

large-scale laboratory scales to prototype conditions.

7.5 Overtopping velocities, distributions and down-fall pressures

7.5.1 Introduction to post-overtopping processes

There are many design issues for which knowledge of just the mean and / or wave-bywave overtopping discharges / volumes are not sufficient, e.g.

• assessment of direct hazard to people, vehicles and buildings in the zone

immediately landward of the seawall;

• assessment of potential for damage to elements of the structure itself (e.g. crown

wall; crown deck; secondary defences);

The appreciation of the importance of being able to predict more than overtopping

discharges and volumes has led to significant advances in the description and

quantification of what can be termed “post-overtopping” processes. Specifically, the

current state of prediction tools for

• the speed of an overtopping jet (or “throw velocity”);

• the spatial extent reached by (impulsive) overtopping volumes, and

• the pressures that may arise due to the downfalling overtopped jet impacting on

the structure’s crown deck.

7.5.2 Overtopping throw speeds

Studies at small-scale based upon video footage (Figure 7.25) suggest that the vertical

speed with which the overtopping jet leaves the crest of the structure (uz) may be

estimated as

i i z c

c u 7 to5

2.5 to2

for non-impulsive conditions for impulsive conditions

where si ghc = is the inshore wave celerity (Bruce et al, 2002).

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wave impulsiveness parameter, h*

m ax . d

im 'le

ss v er tic

al th ro w s pe ed , u

z/c

i Figure 7.25 Speed of upward projection of overtopping jet past structure crest plotted with

“impulsiveness parameter” h* (after Bruce et al., 2002)

7.5.3 Spatial extent of overtopped discharge

The spatial distribution of overtopped discharge may be of interest in determining zones

affected by direct wave overtopping hazard (to people, vehicles, buildings close behind

the structure crest, or to elements of the structure itself).

Under green water (non-impulsive) conditions, the distribution of overtopped water will

depend principally on the form of the area immediately landward of the structures crest

(slopes, drainage, obstructions etc.) and no generic guidance can be offered (though see

Section 7.5.2 for information of speeds of overtopping jets).

Under violent (impulsive) overtopping conditions, the idea of spatial extent and distribution

has a greater physical meaning − where does the airborne overtopping jet come back to

the level of the pavement behind the crest? The answer to this question however will (in

general) depend strongly upon the local wind conditions. Despite the difficulty of directly

linking a laboratory wind speed to its prototype equivalent (see Section 7.3.6) laboratory

tests have been used to place an upper bound on the possible wind-driven spatial

distribution of the “fall back to ground” footprint of the violently overtopped volumes

(Pullen et al., 2004 and Bruce et al., 2005). Tests used large fans to blow air at gale-force

speeds (up to 28 ms-1) in the laboratory. The resulting landward distributions for various

laboratory wind speeds are shown in Figure 7.26. The lower (conservative) envelope of

the data give the approximate guidance that 95% of the violently-overtopped discharge

will land within a distance of 0.25 × Lo, where Lo is the offshore (deep water) wavelength.

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dimensionless landward distance x/L0

fr ac tio

n of d is ch ar ge fa lle

n by d is ta nc e x/

approx. lower (worst case)

envolope

c. 90% of discharge falls

within 0.2 × wavelength

c. 95% of discharge

falls within

0.25 × wavelength

Figure 7.26 Landward distribution of overtopping discharge under impulsive conditions. Curves

show proportion of total overtopping discharge which has landed within a particular

distance shoreward of seaward crest

7.5.4 Pressures resulting from downfalling water mass

Wave impact pressures on the crown deck of a breakwater have been measured in smalland large-scale tests (Bruce et al., 2001; Wolters et al, 2005). These impacts are the

result of an impacting wave at the front wall of the breakwater generating an upwards jet

which in turn falls back onto the crown deck of the structure. Small-scale tests suggest

that local impact pressure maxima on the crown deck are smaller than but of the same

order of magnitude as wave impact pressures on the front face. For high-crested

structures (Rc / Hm0 > 0.5), pressure maxima were observed to occur within a distance of

∼1.5 × Hm0 behind the seaward crest. For lower-crested structures (Rc / Hm0 < 0.5) this

distance was observed to increase to ∼ 2 × Hm0. Over all small-scale tests, pressure

maxima were measured over the range

mgH

p

with a mean value of 8 7.33

The largest downfall impact pressure measured in large-scale tests was 220 kPa (with a

duration of 0.5 ms). The largest downfall pressures were observed to result from

overtopping jets thrown upwards by very-nearly breaking waves (the ''flip through''

condition). Although it might be expected that scaling small-scale impact pressure data

would over-estimate pressure maxima at large scale, approximate comparisons between

small- and large-scale test data suggest that the agreement is good.

7.6 Uncertainties

Wave overtopping formulae for vertical and steep seawalls depend on the type of wall

which is overtopped and the type of wave breaking at the wall. The wave overtopping

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formulae used are however similar to the ones used for sloping structures such as dikes

and rubble mound structures. Therefore, again the same procedure is suggested as used

already for Sections 5.7 and 6.3.7.

The uncertainty in crest height variation for vertical structures is different from sloping

structures and should be set to about 0.04 m. All uncertainties related to waves and water

levels will remain as discussed within Section 5.7. Similarly, the results of these additional

uncertainties have little influence on the results using the model uncertainty only. This is

evident from (e.g.) Figure 7.10 for impulsive conditions at a plain vertical wall.

Resulting probabilistic and deterministic design parameters are summarised in

Table 7.3.

Table 7.3: Probabilistic and deterministic design parameters for vertical and battered walls

Type of wall Type of breaking Type of formula Probabilistic par. Deterministic par.

Plain vertical non-impulsive Eq. 7.4 a = 0.04; b = -2.62

a = 0.04;

b = -1.80

impulsive Eq. 7.6 a = 1.48⋅10

b = -3.09

b = -3.09

emergent toe, impulsive Eq. 7.10

b = -2.69

b = -2.69

Composite non-impulsive Eq. 7.4 a = 0.016; b = -3.28

a = 0.016;

b = -2.75

impulsive Eq. 7.12 a = 4.10⋅10

b = -2.91

b = -2.91

It is noteworthy that only uncertainties for mean wave overtopping rates have been

considered here (as per previous sections dealing with uncertainties). Other methods

discussed in this chapter have not been considered per se, but can be dealt with using the

principal procedure as discussed in Section 1.5.4.

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Armour Protective layer of rock or concrete units

Composite sloped seawall A sloped seawall whose gradient changes

Composite vertical wall A structure made up of two component parts,

usually a caisson type structure constructed on a

rubble mound foundation

Crown wall A concrete super-structure located at the crest of a

sloping seawall

Deep water Water so deep that that waves are little affected by

the seabed. Generally, water deeper than one half

the surface wavelength is considered to be deep

Depth limited waves Breaking waves whose height is limited by the water

depth

Crest Freeboard The height of the crest above still water level

Impulsive waves Waves that tend to break onto the seawall

Mean overtopping discharge The average flow rate passing over the seawall

Mean wave period The average of the wave periods in a random sea

state

Model effects Model effects occur due to the inappropriate set-up

of the model and the incorrect reproduction of the

governing forces, the boundary conditions, the

measurement system and the data analysis.

Normal wave attack Waves that strike the structure normally to its face

Oblique wave attack Waves that strike the structure at an angle

Overflow discharge The amount of water passing over a structure when

the water level in front of the structure is higher than

the crest level of the structure

Peak overtopping discharge The largest volume of water passing over the

structure in a single wave

Reflecting waves Waves that hit the structure and are reflected

seaward with little or no breaking

Return period The average length of time between sea states of a

given severity

Run-up The rush of water up a structure or beach as a

result of wave action.

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Scale effects Scale effects occur due to the inability to scale all

relevant forces from prototype to model scale

Sea dike Earth structure with a sand core covered by clay,

sometimes covered by asphalt or concrete.

Shallow Water Water of such a depth that surface waves are

noticeably affected by bottom topography.

Customarily water of depth less than half the

surface wavelength is considered to be shallow

Significant wave height The average height of the highest of one third of the

waves in a given sea state

Toe The relatively small mound usually constructed of

rock armour to support or key-in armour layer

Tolerable overtopping discharge The amount of water passing over a structure that is

considered safe.

Wave return wall A wall located at the crest of a seawall, which is

designed to throw back the waves

Wave steepness The ratio of the height of the waves to the wave

length

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Ac = armour crest freeboard of structure [m]

B = berm width, measured horizontally [m]

Bt = width of toe of structure [m]

Bh = width of horizontally schematised berm [m]

Bov = longitudinal extension of overtopping front [m]

Br = width (seaward extension) in front of main vertical wall of recurve / parapet /

wave return wall section [m]

c = wave celerity at structure toe [m/s]

Cr = average reflection coefficient (= i0,r0, m/m ) [- or %]

CF = Complexity-Factor of structure section, gives an indication of the complexity

of the structure section, can adopt the values 1, 2, 3 or 4 [-]

Dn50 = nominal diameter of rock [m]

Dn = nominal diameter of concrete armour unit [m]

D(f,θ) = directional spreading function, defined as: [°]

S(f, θ) = S(f). D(f,θ) met ∫

θ)dθD(f, = 0

f = frequency [Hz]

fp = spectral peak frequency

= frequency at which Sη(f) is a maximum [Hz]

fb = width of a roughness element (perpendicular to structure axis) [m]

fh = height of a roughness element [m]

fL = centre-to-centre distance between roughness elements [m]

g = acceleration due to gravity (= 9,81) [m/s²]

Gc = width of structure crest [m]

h = water depth at toe of structure [m]

hb = water depth on berm (negative means berm is above S.W.L.) [m]

hdeep = water depth in deep water [m]

hr = height of recurve / parapet / wave return wall section at top of vertical wall [m]

ht = water depth on toe of structure [m]

H = wave height [m]

H1/x = average of highest 1/x th of wave heights [m]

Hx% = wave height exceeded by x% of all wave heights [m]

Hs = significant wave height defined as highest one-third of wave heights

Hm0 = estimate of significant wave height from spectral analysis = 0m4 [m]

Hm0 deep = Hm0 determined at deep water [m]

Hm0 toe = Hm0 determined at toe of structure [m]

k = angular wave number (= 2π/L) [rad/m]

k = multiplier for mean discharge giving effect of recurve wall (Chapter 7) [-]

k’, k23 = dimensionless parameters used (only) in intermediate stage of

calculation of reduction factor for recurve walls (Chapter 7) [-]

Lberm = horizontal length between two points on slope, 1.0 Hm0 above and 1.0 Hm0

below middle of the berm [m]

Lslope = horizontal length between two points on slope, Ru2% above and 1.5 Hm0

below S.W.L. [m]

L = wave length measured in direction of wave propagation [m]

L0p = peak wave length in deep water = gT²p/2π [m]

L0m = mean wave length in deep water = gT²m/2π [m]

L0 = deep water wave length based on Tm-1,0= gT²m-1,0/2π [m]

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m = slope of the foreshore: 1unit vertical corresponds to m units horizontal [-]

m*, m = dimensionless parameters used (only) in intermediate stage of

calculation of reduction factor for recurve walls (Chapter 7) [-]

mn = ∫

f f nS(f)dff = nth moment of spectral density [m²/sn]

lower integration limit = f1 = min(1/3.fp, 0.05 full scale)

upper integration limit = f2 = 3.fp

mn,x = nth moment of x spectral density [m²/sn]

x may be: i for incident spectrum

r for reflected spectrum

Now = number of overtopping waves [-]

Nw = number of incident waves [-]

P(x) = probability distribution function

p(x) = probability density function

Pc = height of vertical wall from SWL to bottom of recurve / parapet / wave return

wall section (i.e. Pc = Rc − hr) [m]

PV = P(V ≥ V) = probability of the overtopping volume V being larger or equal to V [-]

Pow = probability of overtopping per wave = Now/ Nw [-]

q = mean overtopping discharge per meter structure width [m3/s/m]

Rc = crest freeboard of structure [m]

RcL = crest freeboard of structure landward side (relative to falling plane) [m]

RF = Reliability-Factor of test, gives an indication of the reliability of the test,

can adopt the values 1, 2, 3 or 4 [-]

R0* = dimensionless length parameter used (only) in intermediate stage of

calculation of reduction factor for recurve walls (Chapter 7) [-]

Ru = run-up level, vertical measured with respect to the S.W.L. [m]

Ru2% = run-up level exceeded by 2% of incident waves [m]

Rus = run-up level exceeded by 13.6% of incident waves [m]

s = wave steepness = H/L [-]

s0p = wave steepness with L0, based on Tp = Hm0/L0p = 2πHmo/(gT²p) [-]

s0m = wave steepness with L0, based on Tm = Hm0/L0m = 2πHmo/(gT²m) [-]

s0 = wave steepness with L0, based on Tm-1,0 = Hm0/L0 = 2πHmo/(gT²m-1,0) [-]

Sη,i(f) = incident spectral density [m²/Hz]

Sη,r(f) = reflected spectral density [m²/Hz]

S(f, θ) = directional spectral density [(m²/Hz)/ ]

t = variable of time [s]

T = wave period [s]

TH1/x = average of the periods of the highest 1/x th of wave heights [s]

Tm = average wave period defined either as:

T = average wave period from time-domain analysis [s]

Tmi,j = average wave period calculated from spectral moments, e.g.: [s]

Tm0,1 = average wave period defined by m0/m1 [s]

Tm0,2 = average wave period defined by 20 /mm [s]

Tm-1,0 = average wave period defined by m-1/m0 [s]

Tm-1,0 deep = Tm-1,0 determined at deep water [s]

Tm-1,0 toe = Tm-1,0 determined at the toe of the structure [s]

Tm deep = Tm determined at deep water [s]

Tm toe = Tm determined at the toe of the structure [s]

Tp = spectral peak wave period = 1/fp [s]

Tp deep = Tp determined at deep water [s]

Tp toe = Tp determined at the toe of the structure [s]

TR = record length or return period of event [s]

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Ts = TH1/3 = significant wave period [s]

V = volume of overtopping wave per unit crest width [m3/m]

Vmax = maximum overtopping volume per wave per unit crest width [m3/m]

v = velocity of overtopping jet at wall detachment point [m/s]

X = landward distance of falling overtopping jet from rear edge of wall [m]

Xmax = maximum landward distance of falling overtopping jet from rear edge of wall [m]

Xqmax = landward distance of max mean discharge [m]

XVmax = landward distance of max overtopping volume per wave [m]

Ws = wind speed (Ws x cos Wd= wind speed onshore component normal to structure) [m/s]

Wd = wind direction-angle of wind attack relative to normal on structure [°]

α = angle between overall structure slope and horizontal [°]

α = angle of parapet / wave return wall above seaward horizontal [°]

αB = angle that sloping berm makes with horizontal [°]

αu = angle between structure slope upward berm and horizontal [°]

αd = angle between structure slope downward berm and horizontal [°]

αexcl = mean slope of structure calculated without contribution of berm [°]

αincl = mean slope of structure calculated with contribution of berm [°]

αwall = angle that steep wall makes with horizontal [°]

β = angle of wave attack relative to normal on structure [°]

η(t) = surface elevation with respect to S.W.L. [m]

γb = correction factor for a berm [-]

γf = correction factor for the permeability and roughness of or on the slope [-]

γβ = correction factor for oblique wave attack [-]

γv = correction factor for a vertical wall on the slope [-]

ξo = breaker parameter based on s0 (= tanα/s01/2) [-]

ξom = breaker parameter based on s0m [-]

ξop = breaker parameter based on s0p [-]

μ(x) = mean of measured parameter x with normal distribution [..]

σ(x) = standard deviation of measured parameter x with normal distribution [..]

θ = direction of wave propagation [°]

ω = angular frequency = 2πf [rad/s]

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overtopping of a long, vertical faced breakwater, Proc 28th Int. Conf. Coastal Engng

(ASCE), Cardiff, pp 2299–2311, World Scientific, ISBN 981-238-238-0

Alberti, P., Bruce, T. & Franco, L. 2001 Wave transmission behind vertical walls due to

overtopping. Paper 21 in Proc. Conf. Shorelines, Structures & Breakwaters,

September 2001, pp 269-282, ICE, London.

Allsop, N. W. H., Bruce, T., Pearson, J., Alderson, J. S. & Pullen, T. 2003 Violent wave

overtopping at the coast, when are we safe? Proc. Conf. on Coastal Management

2003, pp 54-69, ISBN 0 7277 3255 2, publn. Thomas Telford, London.

Allsop, N. W. H., Bruce, T., Pearson, J., Franco, L., Burgon, J. & Ecob, C. 2004 Safety

under wave overtopping – how overtopping processes and hazards are viewed by

the public. Proc. 29th Int. Conf. on Coastal Engng. Lisbon. pp 4263-4274.

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people and property from wave overtopping at coastal structures. Proc. Conf.

Coastlines, Structures and Breakwaters, 20-22 April 2005, ICE, London.

Allsop, N. W. H., Lihrmann, H., & Netherstreet, I. 2002 Wave breaking on/over steep

slopes. Paper 16a in “Breakwaters, coastal structures & coastlines” ICE, ISBN 0

7277 3042 8, pp 215-218, publn Thomas Telford, London.

Allsop, N. W. H., Besley, P. & Madurini, L. 1995 Overtopping performance of vertical and

composite breakwaters, seawalls and low reflection alternatives. Paper 4.7 in MCS

Project Final Report, University of Hannover.

Allsop, N. W. H., Bruce, T., Pearson, J. & Besley, P. 2005 Wave overtopping at vertical

and steep seawalls. Proc. ICE, Maritime Engineering, 158, 3, pp103–114, ISSN

Aminti, P. L. & Franco, L. 1988 Wave overtopping on rubble mound breakwaters. Proc.

21st Int. Conf. on Coastal Engng. Torremolinos. 1988

Asbeck, W. F. Baron van, Ferguson, H. A., & Schoemaker, H. J. 1953 New designs of

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Conf. on Coastal Engng. Lisbon. pp. 4301 - 4313.

Stewart, T., Newberry, S., Latham, J-P & Simm, J. D. 2003 Packing and voids for rock

armour in breakwaters. Report SR 621, HR Wallingford.

Stewart, T., Newberry, S., Simm, J. & Latham, J-P. 2002 Hydraulic performance of tightly

packed rock armour - results from random wave model tests of armour stability

and overtopping. Proc. 28th Int. Conf. on Coastal Engng. Cardiff. pp 1449-1461.

Stickland, I. W. & Haken, I. 1986 Seawalls, Survey of Performance and Design Practice.

Tech Note No. 125, ISBN 0-86017-266-X, Construction Industry Research and

Information Association (CIRIA) London.

Sutherland, J. & Gouldby, B. 2003 Vulnerability of coastal defences to climate change.

Proc. ICE, Water & Maritime Engineering Vol. 156, Issue WM2, pp 137–145

(Thomas Telford, London).

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Rough Slopes. Coastal Dynamics, pp. 599-613.

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Wellenauflaufs. Mitt. des Franzius-Instituts. No. 53. pp. 1-245

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EurOtop Manual

Van der Meer, J. W., Snijders, W. & Regeling, H. J. 2006 The wave overtopping

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EurOtop Manual

A Structure of the EurOtop calculation tool

EurOtop Manual

EurOtop Manual

To complement the EurOtop manual, a website has been designed to simplify the

empirical formula by giving the user a choice of standard structures to calculate

overtopping rates. The EurOtop calculation tool can be found at

http://www.overtopping-manual.com.

It is intended for with basic structures only for more complex situations please use the

software PC Overtop or use the neural network.

Calculation tool home page

The introduction page contains a list of the most popular structures and the methods

available to calculate overtopping discharge. PC Overtopping and the neural network

method instructions are describes elsewhere in the manual.

To calculate overtopping discharge click the empirical method link next to the desired

structure or alternatively select the Empirical Methods tab for a full list of structures.

EurOtop Manual

Empirical Methods Page

The empirical method page contains most structure types currently available. These are

designed to follow the guidelines set out in Chapters 5-7 of the manual. If no basic type

exists for your desired structure then use one of the other methods by selecting the

introduction tab (Refer to Chapter 4).

To calculate overtopping rates click the relevant structure type.

EurOtop Manual

Overtopping calculation

Once a structure type has been chosen the calculation page will be displayed.

1. Input

Each structure type will have different input variables and all require a wave period,

freeboard and wave height. The wave period, T, can be input either as a mean (Tm), peak

(Tp) or Tm-1,0. This spectral period Tm-1,0 gives more weight to the longer wave periods in

the spectrum and is therefore well suited for all kind of wave spectra including bi-modal

and multi-peak wave spectra.

The freeboard (Rc) is simply the height of the crest of the wall above still water level. A

wave height at the toe of the structure (Hm0) is also needed for most calculations. Sloped

structures also contain a reduction factor (γ). A range of materials are listed along with

armour based slopes. Please refer to the manual for guidance if no material type exists

for your structure.

All variables must be entered before an overtopping rate can be calculated, for help on

any variable please refer to the manual.

An example Input screen for a vertical wall structure is shown below.

EurOtop Manual

2. Output

There are two outputs from the calculations, an overtopping rate and a structure specific

comment about the calculation method.

The overtopping rate is listed as metres / second mean overtopping discharge per meter structure

width [m3/s/m]

The comment box will list any observations or errors from the formulae, these can range

from wave breaking type (sloped structures) to impulsive waves (vertical structures)

For interpretation of the results please consult the Eurotop manual.

EurOtop Manual

B Summary of calculation test cases.

EurOtop Manual

EurOtop Manual

EurOtop case study number: A

Location:Blyth Sands, Outer Thames, UK

Location

The seawall (cross-section 16) is on the south bank (north and west facing) of the Thames estuary

opposite Thames Haven. Cross-section levels below derived from LIDAR.

Seawall section: CS 16

• Approach slope: approx. 1:100: embankment slope angle: 1:4.5 (cot α = 4.5)

• Embankment crest level: + 5.73 m ODN; toe: +0.2 mODN

• Plan orientation: 344° N

• Rip-rap roughness on embankment seaward face

C h a in a g e (m )

le v a ti o n

m

S c h e m a tis e d X S -1 6

Water levels and wave conditions

Wave conditions from analysis point AP 16 at 1:1000 year joint probability conditions

Wind

direction

Water

level

(mODN)

Hs (m)

Tp (s)

Wave

dirn.

EurOtop Manual

EurOtop case study number: B

Location:CAR3956, Southend, Outer Thames, UK

Location

The seawall faces south and south-west into the Thames estuary about 2km east of Southend Pier.

Seawall section:

• Vertical seawall with small (0.3m) bullnose behind shingle upper beach, mud flat lower

beach

• Seawall crest at +5.7mODN (with bullnose) or +5.4mODN (without bullnose); Lower

beach slope: approx. 1:100: shingle beach slope angle: 1:10 (cot α = 10)

• Shingle beach toe at +0.2mODN, beach crest: + 5.2 m ODN (healthy condition); or at

+4.2mODN (eroded condition); beach crest width: 30m

• Plan orientation: facing 180° N

Water levels and wave conditions

Wave conditions and water levels for 1:200 joint probability conditions, no climate change:

Waves from approximately 120oN

Water level

(mODN) Hs (m) Tm (s)

Conditions with 50 years climate change:

Waves from approximately 120oN

Water level

(mODN) Hs (m) Tm (s)

EurOtop Manual

EurOtop case study number: C

Location: Dock Exit Seawall, Dover harbour, UK

Location

The Dock Exit Seawall seawall forms a revetment protection to

the dock exit road within Dover Harbour. It faces approximately

south (180°N). The revetment adjoins a North – South quay

wall formed by part cylindrical caissons.

The seawall must provide overtopping protection to vehicular

traffic leaving the docks.

Seawall section:

Water levels and wave conditions

Wave conditions at joint probability conditions:

Return

period

(years)

Water level

(mOD) Hs (m)

Tm (s)

Climate change sea levels applied.

EurOtop Manual

EurOtop case study number: D

Location: St. Peter-Ording, North Sea, Germany

Location

The seadike (cross-section Böhl/Süderhöft 3) is on the west side of the Eiderstedt peninsula (facing

west) of the North Sea Coast north of the Eider river. Cross-section levels below were derived from

Seadike section: Böhl/Süderhöft 3

• Approach slope: horizontal (high foreland): dike slope angle: 1:8 (cot α = 8.0)

• Dike crest level: + 7.38 mNN; toe: +3.0 mNN

• Plan orientation: 315° N

• Grass covered dike, no berm

• Width of crest: 3.50 m

Station [m]

ei gh t [m

1:8 slope

Seaward sideLandward side

Water levels and wave conditions

Wave conditions from analysis point Husum at different return periods

Return

period

(years)

Water

level

(mNN)

Hs (m)

Tp (s)

Wave

dirn.

EurOtop Manual

EurOtop case study number: E

Location: Norderney, North Sea, Germany

Location

The historical revetment is situated on the North coast of the island of Norderney, protecting the city

of Norderney.

Seadike section: Kaiserwiese / Norderney

• Approach slope: 1:50: Basalt stone slope angle: 1:4.5; S-profile slope 1:2.4; first

promenade slope: 1:10; roughness element slope: 1:3; upper promenade slope:

• Dike crest level: + 10 mNN; toe: -1.27 mNN

• Plan orientation: 315° N

• Revetment covered with multiple berms, natural blocs, roughness elements

• Width of crest: 5.0m

Wave overtopping for the historical revetment of Norderney was analysed by large scale

model tests (scale factor 1:2.75) (Schüttrumpf et al., 2001).

Water levels and wave conditions

Wave conditions from wave measurements offshore were analysed. Design water level

(DWL) is given by local guidelines. Highest water level (HWL) was measured 1962.

Return

period

(years)

Water

level

(mNN)

Hs (m)

Tp (s)

Wave

dirn.

EurOtop Manual

EurOtop case study number: F

Location: Samphire Hoe, Dover, UK

Location

This structure formed part of the channel tunnel works and is a park now containing the excavated

spoil from the tunnel. The vertical wall and promenade were designed knowing they were going to

overtop regularly.

Vertical wall section: Samphire Hoe

• There is a flat chalk platform in the approach to the seawall. The rock berm is

approximately 2.25m thick (from the toe at -2.42mODN to -0.17mODN)), the front

is constructed from Larsen piles (to +4.2mODN), a plain concrete wall (to

+6.97mODN) and the crest is specified at the top of a parapet wall at (+8.22mODN).

• Plan orientation: 090° N

Water levels and wave conditions

Wave conditions and water levels are at the toe of the structure

Water

level

(mODN)

Hm0

(m)

Tm-1,0

(s)

Wave

dir.

EurOtop Manual

EurOtop case study number: M

Location:DKM5759, Bundoran, Donegal bay, Ireland

Location

Waves from Atlantic storms approach Donegal Bay from 200°N to 320°N. Because of the

sheltering effects of the headlands to the north and south of the bay, the highest waves that

approach Bundoran are usually from the west, 270°N. The proposed revetment is formed

along a tidally exposed shoreline within the bay. Waves reaching the revetment were

assumed to be fully refracted, travelling parallel to the bed contours and not significantly

effected by offshore wave direction.

Seawall section:

1:1.5 slope rock revetment with access steps to a berm with walkway used for public access.

A further 1:1.5 slope runs up to a recreational area approx. 8m in front of the building line.

• Crest of revetment (1.3m wide) +7.9mHMD approx. 8m in front of building.

Recreational area approximately 8m in front of building at +8.6mMHD. Walkway

level +5.5mMHD, 2.9m wide; Lower seabed at +1.0mMHD, slope: foreshore approx.

1:50 – 1:80 rock platform.

• Timber staircase over the lower revetment slope leading to concrete or asphalt

walkway.

• Rock armour (2 layer) on both lower and upper slopes 450kg to 1500kg.

Water levels and wave conditions

Wave conditions and water levels for 1:1yr, 1:50yr and 1:200 joint probability conditions,

including sea level rise of 0.2m over 50yrs.

Wave conditions for 1:1 year event were used to assess overtopping discharge at the

intermediate walkway level (at +5.5mMHD) to evaluate public safety (with a discharge limit of

q ≤ 0.1 l/s/m).

The 1:200 year conditions were used to evaluate overtopping discharge at the building line

(discharge limit set at q ≤ 0.03 l/s/m).

Joint

Return

period

Water level

(mMHD) Hs (m) Tm (s)

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